Make sure you are well ventilated, ideally using one or many fans. That made huge difference for me on the trainer. Are you using a power meter to measure the power output or some other method? Supposedly the cycleops fluid trainers get harder as they heat up, so if you are using speed as a proxy then you should make sure to keep that effect in mind. If you think it might be psychological maybe try listening to music or something like that during your intervals and see if that lets you go for longer. Or you might try some L5 intervals, since those are shorter. If you can do an L5 interval on the trainer but can't do an L4 one, that would seem to indicate that you are just having trouble mentally with the longer intervals. This definitely happens to me from time to time. For whatever reason I give up on an interval, usually early on around the 5 minute mark or so, because I don't think I can take the pain for that long. I just recover a bit more and then try again and usually I can complete the interval as desired (meaning I was just too much of a panzy the first time). A lot of times I think at the 5 or 10 minute mark that I am completely toast, but I keep at it and it gets easier mentally in the second half because I know I don't have to suffer for too much more time. I think maybe playing songs can let me break the interval down into shorter intervals (i.e. I always can just focus on making it to the end of a given song, rather than worrying about the next 15 minutes of pain).
If you aren't using a powertap then there isn't a good way to be sure that your trainer doesn't have some kind of problem. Maybe you could borrow a friend's trainer?
I do all of my hard training on the trainer (I suck at riding on the road, and my hours on the road are 100% devoted to increasing skill and bike handling). In about a month I might be able to get a powertap, so I don't know if I can produce more power on the road than on the trainer. I actually had the impression that all things being equal, it should be easier to produce power on the trainer since you can have a more steady output of power and don't have to worry about where you are going. That said, you will never be as well cooled as you are on the road, at least when the weather is cool.