The implication here is that each individual discoverer must start from nothing but a bag of crying cells, and build up knowledge in a linear order before making a discovery in a vacuum.
In reality, I find we have an entire interwoven society trying to make the discoveries, not independent individuals. There is an entire section of society dedicated to distilling the human essence into teaching. There is an entire section devoted to building infrastructure to make it easier to step beyond. There is an entire section devoted to getting discoverers together, so that they don't ALL have to learn ALL of the knowledge; they merely need to have all of the knowledge when they put their minds together.
Consider that the trade knowledge needed to run a particle accelerator is equally essential to discovery as the quantum physics models used to point the accelerator in new and exciting directions. The physicists probably don't know how to correctly shim the hundreds of segments of the accelerator to be in a perfect shape (and doesn't have the time to learn). The physics probably hasn't spent enough time with high voltage to wire up thousands of electromagnets without a short taking the entire accelerator down. This knowledge, held in the minds of the tradesmen who support the physicists, is equally essential but the physicists never had to learn them; these skills were learned in parallel by all of humanity.
The only thing I have found which can leave us with no time to discover is society itself. If society dulls, and our lives suddenly require an entire lifetime of learning just to survive, that could be the cusp where humanity simply cannot learn any further. However, even then there is a light at the end of the tunnel. The poets have a long list of skills like "how to love" which take a lifetime to learn, and yet we keep working on them day after day. Perhaps one day, discovery will simply take the form of loving the universe and seeing what it wishes to tell us today.
Oh fine! Lets see some math
Lets try to put some mathematical equations down to make sure we're all on the same page. I'll use it to show how a rather boring society resembling the Vulcans could go about never ending discover
First off, I am going to assume there is a never ending supply of things to discover in the universe. If there is a finite number of things to discover, then it is trivial to show that the number of discoveries humankind can make is finite. Let us define the universe of potential discoveries to be $\mathbb{D}$
I am going to assume the only thing in our brain that matters in the long run are structures. These are structures you have to learn over time in order to effectively do a task, such as discovering a new direction. I believe there is more to the brain, but I think this is close enough to model your question of learning and technology. Let us define these structures to be $\mathbb{S}$, the set of all helpful structures that the human brain can possibly organize into, and let $\text{Fits}(S), S\in \mathbb{S}$ to be a predicate that returns true if the set of structures $S$ would fit into a single human brain, and false otherwise. Because entering the world with new structures makes it trivial to prove we can keep discovering, we can assume $S$ of a newborn is $\emptyset$.
Now we need a notation for learning. I will assume, for simplicity, that people learn at a constant rate through their entire lives. I leave it to the reader to show that handling the case where learning rate is variable is a trivial transform from this simpler case. Because I am arguing that we will never run out of things to learn, I can assume the worst case of "you can only learn one thing at a time" without loss of generality. Consider the universe of learning activities, $\mathbb{L}$. For any learning activity $l \in \mathbb{L}$, we can define a function $\text{cost}_{\text{learn}}(l, S)$ which defines the cost (in time) of doing learning activity $l$ given that you already have all of the structures $S$ in your head. Let $\text{results}_{\text{learn}}(l, S)$ be a function which returns a set of structures in your brain after doing a learning activity.
Finally, we need a notation for discovery. $\text{cost}_{\text{discover}}(d, S)$ is the cost of discovering a particular element of $\mathbb{D}$.
Now we can define the goals. Let us define $\text{cost}_{\text{schooling}}(L)$ and $\text{results}_{\text{schooling}}(L)$ where $L$ is an ordered set of learning activities to be the cost and results of raising an individual up from $S = \emptyset$ through a sequence of learning activities. Thus $\text{cost}_{\text{schooling}}$ will be the sum of $\text{cost}_{\text{learn}}$, and $\text{results}_{\text{schooling}}$ will be the final result at the end of iterating $\text{results}_{\text{learn}}$. Our goal is to prove that there can always be a $\text{cost}_{\text{schooling}}(L) + \text{cost}_{\text{discover}}(d, \text{results}_{\text{schooling}}(L)) < \text{lifespan}$. Let us assign this a predicate: $\text{DiscoveryCapable}(L, D_{prev} \Leftrightarrow \exists_{d\in\mathbb{D},L^\prime}[(\forall{l\in L^\prime} l\in L)\land d\notin D_{prev}]$, which is a mouthful to day "A society is DiscoveryCapable if, for their set of known learning activities, and previously discovered disoveries, there exists a discoverable thing." Let us also add $\text{Discoverable}(L, d) \Leftrightarrow \exists_{L^\prime} \text{cost}_{\text{schooling}}(L^\prime) + \text{cost}_{\text{discover}}(d, \text{results}_{L^\prime}) < \text{lifespan}$, or "A discovery is discoverable if, given the known set of learning activities, someone can discover it in a lifetime."
Now here we will note that $\forall_{l\in\mathbb{L}}l \in \mathbb{D}$, or in words, every learning activity is something which can be discovered. This leads to a "Lotus Eaters" situation, where could simply continuously develop new ways to learn without going anywhere, so lets fix that. Lets define $\text{Trivial}(l)$ to be true if $\forall_{S\in populace}\exists_{L_0} (\forall_s s\in \text{results}_{\text{learn}}(l, S) \to \text{results}_{\text{learn}}(l, S_0)) \land \text{cost}_{\text{learn}}(L) \ge \text{cost}_{\text{schooling}}(L_0) $. In other words, its trivial to develop a new learning activity which doesn't teach anything new and costs more than an existing schooling!
Now we do a proof by contradiction. We assume $\text{DiscoveryCapable}(L, D_{prev})$ is false for our society. We will prove this is contradictory, meaning there is no such society that cannot find a discovery.
If $\text{DiscoveryCapable}$ is false, then that means there are no new non-trivial learning activities which are discoverable. If we find that there must be a non-trivial learning activity to discover, we have a proof by contradiction. This means we must prove $\forall_{L, D_{prev}}\exists_l \lnot \text{Trivial}(l) \land \text{Discoverable}(L, l)$
Consider the Turing machine, which is accepted to be far simpler than even a human. If we can prove that, at this time, a Turing machine can develop a new useful learning activity for us, then we can make a discovery simply by following that program. We are, after all, at least as impressive as computers.
Let us devise a turing machine to help. Select a subset of $L$ called $L_T$ which is the learning activities which can be analyzed by a Turing machine. We want to find a program which finds a $l \notin L_T$ such that $\lnot \text{Trivial}(l)$. The first step is easy. It is trivial for computers to find an activity $\exists_{l\in 2^{L_T}} l \notin L$. Such power set behaviors occur all the time in NP problems.
Now what if the computer can't do this? The next step is to gather some data about the universe. If we can't find any new data, then we are literally out of things to discover. If we find new data, we can have the computers crunch it harder, to find things that we don't understand, but computers can find. If they cannot, then all Turing-capable learning methods are exhausted, and we have covered the universe with our computational prowess. We, in effect, used computers to extend our life, crunching a subset of our possible learning activities, in hopes of finding a new one.
And now we sit back and look at the non Turing learning activities. It is not easy to tell if there is a faster way to learn such things. In fact, the only limit seems to be creativity.
The only limit for our capacity to discover is our own creativity.