Memory doesn't work that way (we think). Mostly because (we think) memory doesn't actually exist. By "we think" I mean "the current scientific understanding available to us in the literature". The truth is that memory is still a mystery. Absolutely nobody understands what memory is or how it works. As such, we don't understand memory nearly well enough to answer your question with any certainty.
However, working off current theories of memory, I'll give a broad answer: If humans lived forever (or a being lived forever but had a human-like brain), then they would be able to remember the most important and/or emotionally-impacting events of their lives forever.
Memory likely doesn't exist. It's not a physical "thing" that can be measured. From what I have available to me, memory is actually a series of firing neurons in the brain. That is, when you remember something, you're just convincing your brain to re-fire that neural pathway that was fired once before. But if memory is a mystery, then willful recollection of past events is basically an enigmatic black-magic box. Whenever we think or feel, neurons push closer together or pull further apart - very slightly. This allows the "signals" between the neurons to be stronger or weaker. Rinse and repeat with the estimated 100,000,000 (hundred million) neurons in the human brain, and you get an absurdly complex pattern of near-infinite pathways. When we say a "memory fades", we mean "that pathway no longer exists", or rather "those neurons are no longer in the right order to be fired again".
As such your question begins with a false assumption: memory does NOT fade across time. It seems like that to us, but it's not true. What's happening is we have more thoughts, experiences, and emotions which pushes and pulls those neurons closer or further away, and the firing patterns change. It's these changes which make it "more difficult to recall" a memory. But that's not the memory fading, it's the brain adapting to new experiences. It's changing neural pathways, not a "fading memory".
But people who experience emotionally-engaging (that is, "ferociously active neural experiences") events are more likely to remember them because those neural pathways were set hard. This can be positive or negative: falling in love or a vicious rape; getting a promotion or being mugged; getting married or getting divorced; a first kiss or losing a friend. Whatever is intense neurally is going to "cement a pathway" - ie, push and pull those neurons in a way that the firing signals are strong. When these "neural pathways" are set, (a) it takes way more effort to change them (either an equally intense experience, like head trauma, or a crap ton of mundane experiences), and (b) people are more likely to continually recall (re-fire and re-cement) those pathways.
By "continually recall" I don't mean "directly think about the experience", but "build upon those pathways by re-firing parts of them". For example, after falling in love, you're more likely to keep kissing, hugging, holding, cuddling, talk with, go on dates/share experiences with that person. So those pathways in your brain are building upon the prior experience. So it is on the negative side: the abused child runs from trusting others, the raped woman avoids mutually shared experiences with men, the PTSD victim has panic attacks, etc. To fall out of love takes a lot (either a "strong" experience, like catching them cheating on you with your best friend, or a lot of weak experiences, like "we just kinda drifted away.... for the last decade"). Similarly, to overcome trauma also takes a lot (either a "strong" experience, such as religious or medically-intervened solution, or a lot of weak experiences, like working day-in and day-out to control and push back the PTSD until it finally disappears).
So, you see, if a human-like brain were to continue indefinitely, so long as that neural pathway holds, the memory will hold. As such the "important things" (ie things you keep thinking / reciting to yourself), and "emotional things" (ie strong experiences) will last indefinitely. It takes new experiences to slowly pull those neurons closer together or further apart.
That's how you can forget what you ate for breakfast but remember that douchebag from 2nd grade like it just happened five minutes ago.
Final Note - you'll never run out of capacity.
If this theory of memory is correct, the brain can hold about 100,000,000! memories (about one hundred million factorial). Most calculators will give you an error or just say "infinity" if you try to calculate that.
A few years ago, for the novelty of it, I did an estimated calculation of this value. I forget what it was precisely, but I was able to estimate that if you formed a trillion memories for every atom in the universe at a rate of a trillion times per second, then after a trillion years you would finally accomplish 1% of the total number of neural pathways your brain could handle at one time.
So no, you'll never "run out of space". There's always room to hold onto what's important while adapting to new experiences ... even if you keep living until the end of the universe :)