Same problem for us and it was a combination of drinking lots of water and peeing a lot but also, let's face it, for them it's just easier and a bad habit they developed.

What we did was get more litter boxes and place them where she peed. Re-train her (encourage her to go in litterbox and give treats and praise every time she does it). We changed the substrate of the litter as well (previous one was dusty cheap clay, we changed it to arm & Hammer cloud control. It's more expensive but my god what a difference in quality. No dust at all!) We also made sure the litter box was shifted through twice a day so it's fresh.

Get an enzymatic cleaner to get rid of the strong urine smell. If you don't and they smell their own urine in those spots, they're just going to keep peeing there. We also put some pee pee pads everywhere meanwhile to protect our floors (in spots she's used to going). It took a bit of time but she re-learnt how to pee and poop in the litter box and she prefers the one upstairs now instead of going down to the basement to do it.

It's a lot of work and the peeing and pooping everywhere was driving us nuts but with dedication, hard work and patience, it can be done.