Fly faster to increase defense (lesser hits means more shields).
Tune up Shieldpower to let them reg faster (at 25 or less they don't reg at all, 100 lets them reg at tripple rate).
Use better Shields (regenerative ones if you like reggen).
Escorts are meant to kill quick (use BOFF abilities for damage and survival) and die fast if not played right (to its advantages).
You want 2 copies of Tac Team
You want 2 copies of Emergency Power to shields
You want the shield redistribute button either on your hotbar or bound to something you use often (like the spacebar).
You also want to slot 1-2x Field Generators to increase your capacity.
And lastly, you want to be running over 50 shield power.
This doesn't mean you need to set the shield power to 50.
This can be from a combination of skill slotting (Warp Core Efficiency, Warp Core Potential & Starship Shield Performance),& boost from Emergency power to shields, whatever your final number is it should be 50 at the barest minimum, but generally it will be higher than that if you have 6 ranks in each of the skills I mentioned as well as at least EPTS 1 running.
Shield regen isn't usually fast enough to make much of a difference during a fight. 200 points out of a 4000 cap means waiting 2 minutes to fully regenerate a shield facing, an eternity in a fight. Instead learn to redistribute shield power as reflex and/or use Tactical Team 1 when you're getting hammered. Then, instead of relying on shield regeneration, carry Emergency Power To Shields to reduce shield damage and give some healing, and carry Transfer Shield Strength and/or Science Team for bulk heals.