So I just started playing Might and Magic VI and I was wondering if the wells that increase stats replenish themselves after a while. The luck well in New Sorpigal let me use it only eight times.

There is a maximum of 8 uses at once, but waiting a few days will replenish the supply (try travelling to another location and then coming back to the well).
Anyway if the stat involved is above 14, the permanent well/fountain is useless.

dr.schliemann is right. It also applies to all the other stat boosting wells such as the ones in Free Haven, Bootleg Bay and Silver Cove. They could only be used early in the game.