There are several contributing factors that play small parts in our troubles, but the real issue is that we are not hardcore, and Ulduar is... well, freaking hard.
Due to the nature of our alliance, it can be really difficult to assemble a consistent group that will raid regularly every week. However, for the first time ever, this isn't really a problem for us. We aren't having a problem with not enough people signing up - we have just the right amount. Ocasionally we have to pull 3 or 4 people from friends, but we always check their gear, and so far they haven't been healers or tanks. We've added quite a few new alliance members this way actually, and so far it's worked pretty great.
There are a handful of people, if that, that are not geared for starter Ulduar. However, the few who are in this category are very solid players that are capable of making up for lower gear based on superior skill. In addition, we've been running heavy on the healing side to facilitate learning the fights better.
All in all, the problem is that there isn't really an identifiable problem from what I can see. In fact, I'm starting to think that we're just expecting a bit too much from ourselves for a group that is only a couple of weeks into Ulduar. We've only been able to take down three bosses, and we still struggle with that third one.
I'm thinking that we need a philosophy change. Instead of banging our heads against the wall on a second night, downing nothing new and just getting frustrated and disappointed, we may just need to back off a bit. Have one night for Ulduar 25, and another night for something else - perhaps 2 teams of Ulduar 10, or Sarth 1d/2d, and the occasional Vault run when available.
I say this because we are not over geared - we are in starter Ulduar gear, and we may just not be ready to progress until everyone has used those first three bosses to get a little better gear wise. We are not familiar with all the details of these fights, and so maybe running Ulduar 10 one night a week will help. Ulduar 10 is ridiculously easy compared to 25 in our experience. Knowing the fights in 10 will not make 25 cake, but it will give us some better experience.