That’s interesting. I have a Brother emb/sewing machine that does the same….it cycles off and on almost constantly. It’s impossible to get more than one or two stitches. I’ve had it to two diff Bro authorized dealers for repair. The first said it was the power supply unit, which is no longer available. No one has mentioned "transformer". The second repair person, this past January, said he cleaned the contact points on the PSU and it was fine. So, I came home to begin sewing quilt blocks together. After a couple of hours, the on/off resetting started again.
I don’t know what option I have other than stealing the PSU from another identical machine, ( which I have). It seems defeating, but this machine is my favorite— so smooth and quiet operation. They do have personalities! Good luck with yours..I guess mine is spare parts. :-)