EXIM - 550 Cannot receive from specified address - Sendgrid
Solution 1:
Your provided information is very lean, not enough to accurately debug the problem, but I can make a few educated guesses and give you some places to look.
Are you sure that the failed attemp was connecting to smtp.sendgrid.com:587? It's acting like your exim connected to port 25, and didn't use a user/pass to try to send, which sendgrid rejected.
It very possibly is on their backend, where they are load balancing authentication across an array of LDAP servers, and one of them has stale information for your user, or one of them hits a resource limit and starts rejecting or timing-out new authentication attempts.
Make sure that YOUR system isn't hitting resource limits and having failed lookups of the user/pass.
Find out if anybody else is having periodic auth issues with smtp.sendgrid.com:587.
I'll add to this answer as you provide more debugging information in your original question, and hopefully we can work towards the ultimate solution.