Most of those little battery maintainers don't have enough juice to keep more than one battery fully charged, especially so if there are parasitic loads present.
I have a two amp maintaner, and I left it for a few months on two 95Ah group 24s that were connected in parallel, but were removed from the RV. It boiled them almost dry and ruined both.
Bought a new set identical, and charged them not connected in parallel, with the same maintainer and had no problem. I then decided to read the manual for the maintainer, and it has a max Ah battery that it will charge & maintain, and two 95Ah together (190Ah) was too much.
So.....I'd suggest having a look at the manual of your maintainer. 3 full sized batteries connected together may be too much, fully charged to start or not.