How long will the Paris Museum pass last?

It's only good for 2, 4, or 6 consecutive days, depending on which you are given.
https://www.parismuseumpass.fr/t-en/faq

You could buy another two-day pass upon your return to Paris - one place to get them is at whichever of the included museums you visit first. Or, you could just pay as you go - you can price out the museums you intend to see to determine whether the pass would be worth it.

Yes, agree with Liz. It will be good for your Day 2 and Day 3 in Paris. IF you were staying over then, you might have a few hours on the morning of Day 4 depending on what time you scan in to your first museum on Day 2. It's actually worth 48 hours.

I'm glad you are spending time in Paris on your return! You can decide at the time if you want to go with another Museum Pass or if you will want to get timed entries to museums of interest. It may be less expensive and less hassle to just purchase single museum entries. IF you think you want a 2nd visit to the Louvre you might need to go ahead and book several weeks out from the day you think you will visit. They do sell out.

Where are you staying when you come back and where are your first Paris nights? In addition to the suggestion of buying it at a museum on your first days in Paris, there may be a Tabac nearby your 1st hotel or the hotel you are staying at for your extra days that will sell the Museum Pass.

I have crunched the museum pass numbers and find that it would be hard to make anything other than the 6-day pass worthwhile because of the way the pricing scheme is structured. The 48-hour one is €55, which means that with most museums ~€10, you'd need to cram 5 or 6 into 48 hours to make it worthwhile.

Bear in mind the clock starts the first time you use it, so if you first use it after lunch on the first day, you have until that time on the 3rd day to use it. If you're really strategic you can make this work. But even I, a hardcore museum fan, cannot cram 5 or 6 museums into 48 hours. The pricing works out much better on the six-day one. Divide the price out by the number of days it covers to see--the 6-day is ~€14/day, while the 2-day is ~€27.50 per day.

The Louvre at €17 is probably the most expensive (save the Catacombs, which is not included in the museum pass). But most are cheaper.

Of course, there is also the benefit of skipping the line for those museums that do not require timed entry, and I haven't yet been post-COVID so I'm not entirely sure how this affects things.

Many find it easier, and possibly cheaper, to simply avoid the museum pass. The museums in Paris are fabulous, but 6 days in a row? I simply purchase the museum tickets I want in advance and use the same entrances as those used by pass holders.

And some of us find the ease of the pass makes it worthwhile to always buy the 72 hour pass.

I don't run a "tally" but just being able to drop into small museums makes it worthwhile for my visits.

I found the ease of just walking in anywhere I wanted to go simpler, too. I always manage to at least break even. Fortunately most of the places I want to go this time are not requiring timed entry anymore. Just the Louvre and the catacombs (which aren't on the pass anyway.)