Ideally, you should try to set up a few choke points that can defend most of your Empire. Place starbases, repair bays, and perhaps other defenses grouped together. They should be able to deal with medium to large forces by themselves if set up properly, and even if they fail it will stall the enemy for a while for you to either recall your fleet or build a second one.
If this is a big problem, Corvettes and Light Frigates are fairly fast and work well together, so having a fleet with these ships as the backbone can respond to crises faster.
If all of that really isn't enough, play Vasari. Late game you can build phase gates to make any planet only one jump away.