I own one. Bought it new in the early 90's. Never had a service manual. However, the main issue that develops with some of these radios is the failure of the capacitor that maintains the memory. It can be replaced easily and I did that a few years ago. When it fails the memory will be lost without power being connected. RS sold a chip that could be installed to give the radio CTCSS decode capability. Mine has one.
Basically it was an OK scanner for its time. Now, not so much. Analog wide band only and limited coverage. Steps are not always consistent with modern channel spacing. I would not waste time repairing it other than the capacitor. I still use mine once in a while. Mostly I just monitor the local fire channels. CTCSS decode is nice. Sensitivity is lower than modern radios.
It looks sort of like a button cell, but it is a cap. Large and round. Not like anything else on the board. Don't recall the value, but its marked on the cap. Very easy to unsolder and replace. I got the replacement from Mouser I think. Can give you more info, but I would have to open up the radio and I don't have time to do that for a few days. PM me if you need more info.
Did Uniden make the Pro-2045 for Radio Shack? I always thought that model (like most of Radio Shacks scanners) was made by GRE.European models are supposed to have 66-88mhz I wonder if there is a big difference? Is it just one freq in a specific mode locking up or all the time no matter what? Might be a birdie. I emailed Uniden about a manual but so far no reply.