I recently tried to acquire a polish 'pay as you go' sim card and was told that the phone
number would only be active for one month.
Depends on the network, but in general, the more you top up, the longer you can make outgoing calls. What happens is that when you buy (for instance) - 50zl of credit, you get 50zl of credit and the ability to make outgoing calls for 180 days.
If you aren't worried about what network you use, get a Play sim card - one top up will give you a year's worth of "ability". Even if you go over the year, you can still receive calls/texts/etc, you just can't do anything "chargable".