Since I travel a lot and don't manage to launder while I travel, I'm afraid I often have half my things 'in the wash' a lot. If I had a less itinerant life, a week's worth (7 pairs of undies, 4 bras, 3 sets of sleepwear) might do it.
As it is, I'd be beside myself if I didn't have about 12 pairs of *clean* undies at any given time. So make that 15 or so at least in use. This ensures I'm never out of clean underwear entirely. I tend to buy them in bunches, every six months or so, about half a dozen at a time. I typically rotate out a half dozen every six months too. Right now, I must have a dozen new stashed away to rotate in later this year, in two installments.
Bras I tend to have fewer of, but less than 7 dependable (as opposed to fun ones) would be difficult. I always make sure there's at least a couple packed away in my travel capsule should I have to leave in a hurry. That's still enough in rotation to last me at least a couple of years apiece in very good condition (I make sure the loosest hooks and strap adjustments fit when I buy them, so I have scope to adjust as it starts to lose elasticity). Good bras at a good price *are* hard to find, so these I plan to replace every couple of years and start to keep an eye out for new ones as the 'expiry date' draws close.
As for sleepwear, 4-5 sets for summer and 3 for winter typically suffices; and I keep 2 pairs aside for travelling again. And I do tend to wear these until they are worn (cotton fabrics mostly, so until they start to rip and fall apart very literally). I just threw out a bunch that have to be over 5 years old I think...The newest I currently have are about a couple of years old.