I'm wondering if I can just postpone paying for a insurance renewal.
You can postpone the non-compulsory aspect, AC or OC, I always mix them up, call or email your company and sort it with them.
Doubtlessly you'll get differing opinions here because not everyone is insured by the same companies.
I wouldn't do it though, if your car is robbed or damaged you'll get nothing and Polish insurance is pretty cheap anyway, better safe than sorry imo