How to tell my professor there's a system issue and remind them of writing the LOR at the same time?
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.