You have a very common problem that occurs in games with humans.
Each of you are relatively equal. The player with the maintenance free fleet has a slight advantage, but given your tech levels by turn 80 I assume you all have fairly large empires,
You must change the balance. Alliances, as suggested, are a good way to do this. Try to be the ganger not the gangee! Better yet, try to ally and avoid any large batttles.
You game will eventually hinge on economics. It doesn't matter if you have a maintenance free fleet if you can't replenish your losses. Attack homeworlds and farm colonies for the organic races. Protect your big resource producing colonies. Also, if you can attack planets with shipyards you will slow the flow of reinforcements.
Use intel to steal ships and overthrow colonies. Don't get into a war of attrition as this will just weaken the two of you and leave you ripe for destruction. Try to convince someone else to join you in an attack on the player with the maintenance free fleet. Then try to avoid combat, let the other guy fight.
Another thing that will have a big effect on the outcome of battles is your fleet strategy. Since you are fighting in strategic mode you cannot excercise your tactical genius. I've noticed that against the AI, if the fleet leader is destroyed the AI freezes for a turn. Use a formation that protects your leader. One free turn of fire can turn the battle your way.
Also, build the facilities that prevent star destruction and nebulea formation in your key systems, if you have the tech. Don't let someone take out entire systems at one time. And do it to them if you can
Good luck and let us know how it plays out.