Good dealer support is what is needed in these situations and it sounds like yours needs a trip to the dealers.

Is the machine only breaking needles when you FMQ or is it also breaking them when you sew standard seams? That would be worth a test to see if maybe the fabric is being pulled too fast.

Yup, you've had lots of good advice, I'd make a trip back to where I bought it !

You've changed needles, are you sure it is up all the way and that the flat side is in the right place?

You are moving to fast is probably more likely the culprit and why you had trouble with your other machine, slow down, do you have a dealer who can show you what you are doing wrong. I had this problem when I moved to fast.

Also - look for some utube videos of demonstrations showing FMQ. I watched a ton when I was starting out.
Along with what everyone else told you, check to make sure you have your machine threaded correctly and the bobbin is going in the correct direction. I have been quilting on mine for 4 years and never had a problem until I put on a new spool of thread (good quality). I couldn't keep the thread from breaking and needles breaking right and left.
I finally put back on the previous thread and no problems. I emailed the mfg and they replaced the thread for me.

When I'm moving the needle up and down without fabric, it seems to be ok. It's very possible that there's too much play between the fabric and needle plate! When the needle goes into the fabric, there's an unusual "pop" like it's really breaking into the material. I'm not sure how to cure this. It's pretty close to the needle plate, and if I lower the rollers anymore, the roller will be laying on the machine. But the fabric is not laying on it, it's hovering 1/4 of an inch (or less) above it. And of course, the quilting foot doesn't hold it down so I think this might be contributing to the problem, but I don't know how to fix it.

I bought it used from an individual. I have been using Schmetz needles so I'll stop using them. There were some Organ needles in the box too, so I'll give them a whirl. The shop charges $100 just to look at them, so I'm trying to avoid that. On the other hand, it seems like a class is in order for me. I just don't know what in the world I'm doing. :( I do plan on taking her off the frame and trying some simple sewing until I get used to her.

I'm sure the nice widower that I bought it from would be willing to email lots of advice, but since we live an hour away from each other, that might make things difficult :) But seriously, he's out of town, but I'll email him next week and ask if his wife had a problem with breaking needles. Hopefully, I'll have it figured out before then.

When I bought my embroidery machine, I went to the Sew n Vac and one of the gentlemen there was really nice and showed me how it worked (I didn't even know how to make it go without a presser foot!!) and was really helpful. But my husband took my old Elna in there and "the other guy", who happens to be the owner, is a whole 'nother character!! I won't say anymore than that, because you just never know who's on the forum... but if it wasn't for that first guy, I'd never step foot in there again, and I sure won't do it when the 2nd guy is there.

TBH, I haven't even tried to make seams with it! I'm going to try that this weekend, and see how she sews. I do have some sewing projects that might be more fun on her than my cheapie Singer Simple anyway. At the risk of sounding really whiny, I paid a LOT of money for her and the ONLY thing I ask of her is to quilt! I had a good sewing machine and I wanted a good quilting machine.
But I can't tell what I'm doing with that frame in the way, so I'm taking her off the frame and putting her on the cabinet and having a good, long talk with her. And I'm going to watch every video on the internet that I can find for machine quilting (FMQ is when you're moving the quilt, right? I'm finding lots about that, but not a "long arm" frame situation like I have.). Anyway, I have her set on slow and I'm barely moving the fabric. I'm not even trying to quilt at this point, just letting it run and seeing when the needle breaks.. see if I can find a pattern, so I don't think it's caused by going too fast. I think that's what was causing it on my other machine, so I'm trying to avoid that.