...and what is solar controller model?
It sounds like his energy use is low, and solar is "almost" doing the job as is. Remaining 5% is mere 11 AH - or less, with what BFL13 noted. Having more panel wattage would help, as the battery would go into Absorb sooner.
Controller should switch to Float for the rest of the day, this is what battery normally wants. But when Float time is not long enough - because it went into Absorb too late - you're left with less than 100% charge. Raising Float to 14.8 for several hours is not good for batteries, and leaving it under-charged for more than 2 weeks isn't good either. Can't say which is better - or how long you can go like this. The longer it goes, the shorter they will last.