How to tell my professor there's a system issue and remind them of writing the LOR at the same time? I'm running into problems of not knowing how to politely remind my professors of writing me the LORs and informing them of a potential technical problem at the same time. 

I recently had a professor who was trying to submit an LOR to University A seven times, but Uni A's system had a technical issue and didn't let him upload the letter at all. He contacted tech support but they never got back to him and, eventually, he gave up and asked me to ask for other professors for letters. This is a very reasonable request since the system was truly frustrating.

My problem is that I don't know if that technical issue will happen to others as well when submitting the letters, but I don't want to wait until the last minute for them to submit the letters and tell me the system doesn't work. It would be very risky. 

So I want to let them know that Univ A's system might have this issue and want to have them trying uploading letters ASAP, so that if there's a problem, I'll have time to fix it. 
But, at the same time, these are the same professors who are writing me letters for other universities, not just for Univ A, and I don't know how to frame the letter to remind them? Will it seem like I rushing them to upload all the letters to all the schools?
Explain it just as you described (avoid acronyms though):

Hello Dr. Smith,
I want to thank you again for agreeing to write LoRs for me for graduate school. This is just a reminder that they're due on December 42nd. Please let me know if you anticipate any difficulties with meeting this date.
In addition, please be aware that the computer system at the University of Mississippi at St. Louis at Berkley at Gondor may be having problems -- at least one of the other individuals I asked for a recommendation has had a problem uploading their LoR. If you have difficulty as well, please let me know as soon as possible so I can get in touch with the university's tech support staff.
Thank you!
Sincerely,
Lavender S.