That is the only problem I have with my 5K Aims inverter also, I think a digital clock radio gained about 4-6hrs over night. It was alot anyway, otherwise it runs everything fine.
Not a real problem for me so I never fixed it. Depending on what the timers are for etc.. a solution may be to find a cheap used sinewave UPS and run it for timers and clocks.
I have done lots of things playing around, some work and some don't. You might be able to run a UPS off the Aims inverter. The UPS might correct the power, clean it, and the clocks/timers then run correctly. Some Ups's will work ok, some may click and clack like they are kicking back and forth. Various combinations have worked for me and others have had strange results also.
I have about 6 Ups's I think and 3 or 4 various size inverters and changed tested alot of ways.
If you don't use the UPS on the batteries they should just stay charged and not much power loss for charging I think. It's still nice to have the backup available for some things incase the batteries get low or overloaded and the main inverter shuts off.
If you go the inverter route you may also be able to just run it off the batteries direct if you want and avoid the main inverter power. I have also done that too of course.