Ok thanks for that info. I would say if the wire size wasn't large enough for the breaker you purchased for them install, they are well within their duty and rights to refuse to install it. That could create a liability issue for them. However, it does seem pretty odd and is very suspect that they replaced it three times without issue. The fact the breaker has been replaced three times is an issue though. A breaker should last a very long time if sized correctly. This is the reason I asked for the unit data and wire size, I would have looked everything up for you and told you what you should have. If the wire size is too small for the unit size and/or the breaker is marginally sized for the unit, heat will develop in the circuit and that is a compressor killer and will also take out breakers.
A four ton unit is a fairly large ac current load (amperage). It would probably call for a 50 or 60 amp breaker and require #8 or #6 copper line wires in the branch circuit respectively. I suspect yours may be smaller. If, for instance, you have a 50 amp breaker on a four ton unit with a branch circuit fed with #10 gauge wire which is rated for 30 or 35 amps depending on wire type, you could easily overload the branch circuit wire causing heat to build up. What happens in that case is the branch circuit line wires become like a resistors and actually start to draw current as a separate load than the compressor. This in turn lowers the voltage available to the compressor and will cause the compressor to run higher amperage as a result.
If breaker replacement gets the unit up and running and cooling good, I'd say my example above is a pretty good bet for the scenario you have. Also, as compressors age, they get less efficient which also causes them to draw higher current (amps). This will only make the situation that much worse. What they are telling you is not a stretch if you have a branch circuit with too small of a wire size. However, if the compressor runs and cools fine, chances are it's fine.
I would suggest having an electrician have a look and if the branch circuit wire size is too small, have them replace the wiring with the proper size. I cannot count how many ac systems I've seen with a branch circuit wire that was too small! It was pretty common many years ago, even in new construction. I remember the code enforcement inspectors on new construction starting to look at and require unit breaker size info for new homes as late as the 90's! Before that, it wasn't really looked at. They didn't start looking at unit branch size data, wire and breaker size in existing hvac replacement applications until the turn of the century! That was in SW Florida too, where ac is very heavily used!
If I were a betting man, from your description of symptoms and what the service company said, I'd bet you have a branch circuit too small and an older ac system that is probably just fine. However a small branch circuit will take its toll pretty quickly on an older ac system (compressor)!
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