If/when a third round of stimulus happens, the verbiage states the 2020 tax return will be used, if available. If it is not available a prior year return will be used.
If your prior year return makes you ineligible for a stimulus payment, but your 2020 return shows you eligible, you do need to file your return.
However, if you are eligible with either return then you will get any stimulus payments you are eligible for.
Additionally, if you post the reject reason in this forum someone may be able to help resolve the issue.
Bottom line: If your e-files keep getting rejected you should print, sign and mail them in.