No advancement at all
Let's assume "very nearly destroyed" (a very vague description) means less than 5% of the population survives every attack. Those attacks occur every 20 years. Let's make an outrageous assumption that the only remaining people are distributed 19:1 in favor of women and all the women are prime childbearing (18-20 years old).
In 10,000 BCE the world population is estimated to be 2.4 million. The late stone age was about 40,000 BCE, let's assume 1 million people. The insects kill 95% of them.
That's 50,000 people: 2,500 men and 47,500 women. Let's be generous and say each woman has an average of 10 children (we're being outrageous, after all) before their bodies simply can't take any more. I'm not going to get too detailed, I'm assuming no generation produces within the time boundary of another. This means that when next the insects come, we have a population of about 525,000. That's HALF of the original count — and that's important.
Because the insects take 95% again. I'm ignoring accidents, war, plague, and anything else that can kill a human. I'm assume 10 kids, no miscarriages, etc. Just the insects.
Now we have only 26,250. Magically, 24,938 are women.
Another cycle. Now we have 13,781...
See the problem? We're being OUTRAGEOUS with humanity in giving them far beyond the normal possibility of surviving. In reality, they're extinct in 200 years. Max tech level: stone age. In fact, they probably regressed.
So, how much damage can my insects do and have growth?
A better child-bearing average is 4. I'm still going to ignore war, accidents, miscarriage, illness, and everything else (completely unrealistic, but enough for government work, as they say). I'm also not going to play the overlap as that woudl require more calculation than I want to put into it. The odds are you have basically a 1:1 distribution of men to women. Realistically, some would be too young to breed, others too old, but let's ignore that, too. How many can the insects take and have any population growth at all?
(1,000,000 * X)*4/2 = 1,000,000
X = 50% MAX!
Anything less than a 50% kill rate and the human race is extinct. It's just a matter of time. In reality, accounting for everything I said I was ignoring, your insects probably can't take more than 40%. I'm going to roll with that.
Now, how much can we take and end up at, say, steam engines? Practical application engines came in the 1700s. Let's say 1700 for easy math. 40,000 - 1700 = 38,300 years. Insects every 20 years. 38,300 / 20 = 1915 generations.
MASSIVE ASSUMPTION: If I end up with 50,000 people, I have a (barely) believable chance of inventing steam engines. So, I start with 1,000,000 and end with 50,000. How many can I take over 1,915 generations to get to this?
I hated my statistics class...
My gut says it's about 42% maximum.
What tech level humans can get to isn't really the question you want to ask. You can get to any tech level if the insects destroy few enough people every 20 years. Therefore, the real question is, how many people can my insects destroy every 20 years and get to a specified tech level?
Steam engines: ~ 42%
Any declining population will result in extinction eventually.
Any advance in technology provides better protection against the insects.
Franly, once we have fire (smoke) + caves, we have a way to save most of the people on every attack.
By the stone age people can protect themselves. I've talked myself out of the believability of this scenario. Sorry.