What year is your 372xp? I never had a hard starting saw like that 2013 550xp, once in a while it started good but most times right from the get go especially if stored a week in vertical position with half tank of gas, two pulls with choke and gas run right out of the exhaust, pull plug yadda yaddy..... then it was suppose to be a 50cc pro-saw not a 4 year disposable saw of part time use.
I found the same thing with my 545... almost identical to your 550 except that mine wasn't an XP. You couldn't walk up a softwood tree limbing it without the saw dying at least once... to restart I had to set the brake, hold the throttle open and drop start it several times.