Of course you can... The chairmen on this game are no way near demanding enough.
How do you mean nowhere near demanding enough? He even uses Moyes as his reference, most clubs sack managers when things are at risk of going really bad. If you're doing a steady job then it won't ever really go bad enough to get sacked, won't go good enough for you to attract interest elsewhere. Most mid-table clubs will stick with their managers until they either get offered a job higher up or until they have a bad spell where nothing seems to work for them with their current club.
Pulis has been with Stoke now for 6 years, having finished 2nd in the championship and runners up in the FA cup he has got a couple of feats to his name regarding it now but hasn't actually won anything. I really don't see our chairman letting him go until he feels he has done all he can.