I don't understand why your father doesn't want to replace the battery, I suppose a quality of life decision.
The battery life expectancy is probably + or - a couple of months if it is designed to run for years.. I assume that is the case.
How the pacemaker stopping would affect your father depends on what his dependence is. If it is there just as a safegaurd against, then it becoming nonfunctional would not have any effect until the need next arrises. That's my guress. In any case I don't think you gave enough information for even an expert (I'm not one) to provide any specific prognosis.
They may not need to replace the leads, they can be detached from the old pacer and put into the new pacer. If they do not need to replace the leads, the surgery will be less elaborate than the initial implant. The pacmaker is just under the skin, in a pocket, easy to get to and service. They almost always replace with a new pacer to take advantage of the newer technology and they get smaller as the years go by.
Personally I think lead placement is most of the battle. Sometimes they do have to replace the leads if they are older technology or fail some basic tests.
If the pacer is at the "elective replacement interval" or ERI, then it probably has sustainable battery life left. They should be able to interogate the pacer to estimate remaing power.
I'm assuming that what you meant by "no underlying rhythm" is that his SA node no longer functions at all and he's 100% pacer dependant. That in mind, the batteries lose enegry slowly. If they start getting low enough, best case scenario will be inconsistent pacing, chest pain, and arrhythmias. There are "backup pacers" in the ventricles which may trigger "escape beats" (if his still function). However there will be no atrial function. Ventricular pacing is not a stable backup system and may degrade quickly into vtach or vfib.
If the pacemaker fails suddenly it can be catastrophic. The more likely case though is that the batteries gradually degrade like the example I provided above.
Tough call there, let us know if he changes his mind.