GN & MT are both correct… It all depends on how “finished” the basement is. If it’s full of gaps or the walls or floor are “soft” enough for mice to dig through, it’s virtually impossible to mouseproof short of a full renovation. If this is the case the best you can do is try to figure out where they are coming in from and plug those holes (quarter size and up). Concrete is great for sealing boiler rooms, a common point of entry. You can also add mouldings (1/4 rounds or whatever fills the gap) between the floor and wall.
If there’s construction nearby that’s probably the reason for the persistence of the problem as they are being disturbed and finding other accommodations. Once the construction is over and you (and hopefully your neighbors) are placing poison, the problem should ease up. I’ve never tried this before but it’s also possible to inject poison into the walls, assuming they’re not solid. I assume you’d need a commercial exterminator for that. Good luck!