E. coli infections or other intestinal bacterial infections can technically cause bleeding because of irritation. but generally with ones this age it's coccidiosis.
You know, I've read that cocci are actually in all dirt samples - whether or not there are poultry there. But I've often wondered exactly HOW cocci get into chick cages that are disinfected and with no bedding, no dirt, etc. I'd really like to look more into that and figure out how that happens.
This might be a great area for dlhunicorn who I bet might know? I'll let you know when I know.
The other thing is that a lot of poultry is, unfortunately, guessing. We really don't know for sure that this even IS coccidiosis without a fecal being done. That being said, even testing fecals for cocci are notoriously hard and many vets treat symptompatically once all other bacteria/worms have been ruled out. It's not easy to get the oocysts to show up on the scope.
In the mean time, I'm so very sorry that you've lost more babies. Please don't blame yourself as this is part of the learning process. That's one of the reasons why I'm so big on giving probiotics early. In my flock, I keep Probios (brand) or whatnot around and if I see anything at all the birds get it. Other than feeding medicated feed and watching for any sign, that's really the best I can do.
I can say that coccidiosis in my flock tended to present whenever conditions were hot, humid, wet, and the chicks pooped in their waterers or feed - or stepped in either. I don't brood my chicks on the ground and they're all started in wire-bottomed cages after the first two days of standing. I disinfect inbetween, but then again I rarely get coccidiosis anymore because of my probiotic program so.. maybe it's exposure to older birds?