Is it common for a cat who is recovering from a UTI to continue leaking?

My family adopted a tom cat about 6 month's ago that we've known for appx. 2 years. I don't know how old he is or his health history. Recently we had to take him to a vet ER for severe dehydration, which we found out was caused by a UTI. We've been medicating him (twice daily) with amoxycillin. He seems to be doing better, but he'll urinate on bedding as well as the litterbox and he's ping light colored blood. Under normal cirstances will he improve? When we took him to the ER vet, he was lathargic and incontinent, and since we've worked hard to keep him hydrated. Also, is there anything someone might recommend to keep him from getting more UTI's (ie. home treatments, dietary changes)? I can't afford anymore $200 vet bills.