"However, when a corporate return has no issue begin electronically filed (the other day) it seems that the whole system is not down. Is it only down for 1040 and 1041?"

Here's what you see on the IRS' MeF status page:

Filing Season Start Dates:

Business tax returns: January 8, 2021

Individual tax returns: TBD

Obviously, their press release is ahead  of their own web status update.