hmm I'm still new.
For me, if the procedure requires u to shut it down in the first place, then leave it shut down. There is a reason why it's been shut down.
If the procedure requires ONLY to retard thrust lever to idle and check parameters then leave it running if parameters/procedures allow.
I remember someone once told me , " if u shut it down then leave it. If it flame out due rain/weather then u can consider to relight. The last thing u want is to turn an engine failure into an engine Fire."