My Connie refit managed it. Granted she blew up more times than I can count, and it was a long, hard battle, but with the right combination of skills and tactics, they are beatable. And such a sense of triumph when you achieve it. If games were so easy you could just walk past everything quickly, there would be no sense in playing.
A Romulan Strike Team, Missing Farmers and an ancient base on a Klingon Border world. But what connects them? Find out in my First Foundary mission: 'The Jeroan Farmer Escapade'
There's also the fact that if you die enough it starts to feel sorry for you and just lets you kill it. Or have they changed that since the last time I had trouble with Warbirds? I swear once you figure out how to kill them the only "challenge" associated with doing so is getting away from the warp core explosion.
Each faction's storyline, at least on the Fed side, is supposed to be a good challenge for the level that the mission is aimed at. Romulans are a bit cheesy, I will admit. I have never seen any other NPC, and definitely no players, utilize both High Yield and Torp Spread on the same attack. It's either that, or they have WAY too many torpedos on one ship.
That aside, you need to learn tactics. You are running a cruiser, so you should have your skills as well as your Boffs and equipment backing your ability to tank. If you don't, then you need to figure out what ship you want to run. Captain level does not have the skill points to be both damage AND tank. This is why most people respec once they hit VA50.
Last piece of advice: If you find yourself getting annoyed at the enemies, take a break from missions and grab that XP grind elsewhere. Come back in about 3 levels or so and you will likely see a difference in what you can do.