I agree it's important to have a therapist I can rely on in crisis, and I believe trying to avoid the ER or other serious measures is an excellent barometer of reasons to call a therapist.

I am blessed, as someone who needed serious work on trusting and being not 110% self-reliant to a fault, that my therapist is always receptive to my emails and will call me as requested. She encourages me to write her anytime I'm struggling. What helps me is that I pay for the calls and emails, as they are in-depth, so I don't worry so much about her resenting the extra time or help, and she is semi-retired, so my struggling at a late-evening hour doesn't disrupt her next day the way it might if she had 10 clients to see.

I really feel lucky to have this arrangement.