I have played a few matches with Carriers and Motherships and have found them to be exceedingly durable -- as long as they listen to what The Rock says and "Know Your Role"!
If the scenario is Call to Arms, attacking a Convoy Raid, or defending Recon Run, I can't advise 'em. However, fights with debris and lots of deployment space are easy to live through. They are fantastic in Space Superiority, Annihilation, and, occasionally, in Assassination. Follow some brutal rules --
-- Hide 'Em!: Why don't you fly 'em into Asteroid Fields? Good question. You probably should; barf out the raiders (typically takes two turns on each), and All Stop, move 1 inch or so, and go meteor diving. Even if you screw up the asteroid roll, remember that if you move 1-2 inches, the GEG will eat most of the damage. Inside of the asteroid field you can only be hit by other ships in the field. You only move, at most, 4". If the opponent is trying to win a race to you, he'll have to move a lot faster than that -- and could easily eat massive asteroid death. Finally, when he enters, you leave -- he still can't shoot you!
Sticking around is risky but possible. On the motherships, those pulsars are twin linked, so you get the CAF effect on the AP weapon. Worth considering.
Dust clouds aren't as satisfactory -- they don't create the damage asteroids do. The denser the field, the better!
-- Jump 'Em!: Carriers only have to stick around for 2 turns. After that, you can just choose to run like heck. Off the board. Though a jump point. It's only 1/4 of the total value of the ship, so no big. Other posters have suggested setting them up facing backwards -- not a bad plan.
-- Supersize 'Em!: If you are flying a 5 Raid fight, just keep in mind the enormous amount of effort it'll take that fleet to kill that Mothership. Only Centauri, Solarhawks, or big Ka'T** stacks can realistically do it, but lucky Hyperions might get a shot at it. It's still 100 points! Put that ship in a 5 War fight in the open and it's like waving a red cape in front of a bull. Put it in front of 5 Raid and they'll ask if shooting it is even worth their time; it's 100 points GEG 4, for G'ness!
-- Wait 'Em!: You move last -- you have lots of skirmish ships and a +5/+6 initiative, for g'ness sake! Use this to best effect.
-- Shield 'Em!: If needed, use some other ships to block. Pick one bad beam or two and jam something else in the way. I hate Maneouver to Shield here with the Raiders as you lose the Dodge trait on the shot, but it's a possibility. The Light Cruiser is the best candidate for this, but that's kind of pricey. This can fail, too, making it a bit of a desparate maneouver.
-- Play on the 4x6 table: It's pretty necessary.
-- Cleanup on Aisle One: Finally, if the fight starts to clean out a bit, your trump starts to show: in smaller fights, the previously hiding mothership can emerge and flatten the remaining ships firely directly. After all, as powerful as they may look, 2 Haliks on their lonesome aren't a threat to pop a Carrier anytime soon. The Carrier can easily win that. The combat value of a Mothership really depends a great deal on the scenario -- a Mothership in a 6-Battle fight isn't nearly as dangerous, point for point, as that same ship in a 5-Raid fight. It's even more so when you have the Raiders make sure the big beam ships are done. It's easier when you make sure the Stormfalcon is gone first. Then mommy can come out to play.
