It depends a lot on a host of factors how long your print developer lasts. There's really no hard & fast time limit to give. You'll have to work out for yourself what works for you (yeah, that story again).
So I can't give a straight answer, but I can give some reflection based on my own experience & practice.
I think it's important to understand the nature of the risk of stretching your print developer. After all, if you know what problems to look out for, you know when to mix fresh developer. What happens with a print developer that's overused or has simply oxidized beyond repair due to old age, is that it simply won't finish developing the print within the pre-determined development time. You'll notice this in the form of a weaker image and particularly weaker blacks in your prints. The darkest area just don't go as dark as they do when you're using fresh developer. So this is the thing you need to look out for.
Sounds simple, but especially if you're just starting out with darkroom printing, I'd recommend making some samples on the paper(s) you use that show the actual dmax of the paper. You can then use such a strip or print as a reference to periodically check if your prints are still coming out OK. The reason is that developer deterioration is a gradual process. Your blacks may start to slip long before you notice if you're not watching closely. Having a known-good reference at hand will allow you to detect this much sooner.
So failure of the print developer is not a black & white situation - it's shades of grey. Literally.
Prints are generally developed to completion, which basically means you develop until there's not visible change in the print if the development time is extended further - within reason. If your determined development time is let's say 90 seconds, then developing for e.g. 120 seconds shouldn't make an appreciable difference. In practice, this means prints are usually developed for a standard time; you determine the development time and then stick to that. I assume this is also how you work.
You can imagine that if your print developer starts to fail, it's possible to simply extend the development time and allow the slow developer to still get the job done. Mind you, there comes a point where the developer simply won't finish and you'll end up with flat prints with weak (often mottled, and brownish) blacks. Until that point (which again is more of a gradual process than a clear cutoff point), you could use
@MattKing's suggestion above w.r.t. the time it takes for a certain part of the image to appear and calculate the required development time on that basis. So for instance, using fresh developer, record the time it takes before a certain midtone to appear and divide your normal (known-good) development time by that duration. E.g. if your normal dev time is 90 seconds and the midtone in question starts to emerge at 30 seconds, this would be 90/30 = 3. You now know that by the time you see that midtone pop up, you're at 1/3 of the development time. If you're working with a well-aged developer and it now takes 40 seconds for that same midtone to start building, you know you have to aim for a total of 120 seconds to get to (more or less) the same point as with the fresh developer and your initial development time. You'll find this approach described in literature as "factorial development" - if you search for this term, you'll find it's recommended for instance as a way to get perfect consistency from print to print when printing editions, but it's in principle also possible to use this approach to extend the life of your print developer.
This is not to say I'd necessarily recommend factorial development for this purpose. I mention it as an option, only. For simplicity's sake, I'd consider (especially when starting out) to remove as many problem factors as possible and just mix fresh developer at the start of a session. At the same time and especially during longer sessions, do the reference thing I explained above to spot problems with the developer running out of steam.
From a personal perspective, my approach is different still. I stick to a system that
for me works consistently enough. In my case, this involves a pretty standard developer (ID62 general purpose developer) that I mix from scratch as a concentrate. I keep a bottle of concentrate as well as a bottle of working strength solution at hand. The working strength solution I replenish from the concentrate. I never calculated a strict replenishment rate and just replenish liberally. This ensures that I have short development times (generally 1 minute up to 90 seconds for some FB papers) and I rely on the principle of develop-to-completion to allow me some leeway in an exact development time - so I just stick to 60 or 90 seconds and verify at the start of the session which time is sufficient to get the job done. If 90 seconds doesn't cut it, I replenish the working strength developer a little more to boost its activity. The working strength developer goes back into its tightly capped glass bottle at the end of the session where it awaits the next session. The last time I mixed a fresh bottle of working strength developer is about 4 years ago when we moved into our present house. Sometimes there's only one or a few days between sessions. Sometimes there's months between uses. But so far it has never failed.
I've done the same thing with ID68 as well and it works similarly. I mix both the
ID68 and the
ID62 from scratch as concentrates (click links for formulas on
@Ian Grant's excellent website). The reason I DIY mix the concentrates is because in the past I've run into problems with half-full bottles of commercial concentrates that sat around for too long and went dead. Apart from the inconvenience, the waste always bugged me. So I now mix relatively small amounts (typically 500ml) of concentrate/replenisher at a time, which I store in a clear glass bottle so I can tell when the concents start to go too dark (which signifies oxidation).
Again, the gist of all this is to figure out what works for you. I'm not going to say that your scheme of re-using your developer across three consecutive sessions will work. Maybe it will, maybe it won't. I want to encourage you to learn to recognize yourself what's going on and how to proceed. You'll get no fish from me, but I hope I've contributed a piece of the tackle you need to catch your own.