While it kills us to see Purab being subjected to Jassi's nakhras, I think his reactions suit well with the character he is portraying(although the whole chauffer bit is taking things to far). Purab is shown as a successful businessman. Such a person is bound to be very patient, persistent and a good strategist. He is never shown to act impulsively and this quality is misunderstood by many as a weakness. I for one think that this is his greatest strength. Do you really believe that a successful businessman such as him would become a doormat for anyone? So why would he go back to Jassi after all the humiliation he is made to suffer?
I think Purab understands where Jassi is coming from. He knows her feelings for Armaan and also realizes that unrequited love is very painful (as he himself knows) and so can understand her reaction and Armaan's manipulations, especially since Jassi is an honest person. Jassi as yet is not ready to face the entire truth behind Armaan's charming faade and Purab knows better than anyone else than to force her to confront this as it might drive her away from him.
While many times we wish he would just knock some sense into Jassi, the fact is that she needs to come to gain this awareness on her own (remember Jassi's reaction when Nandu defended Purab) by learning from her mistakes and successes. To me it seems that Purab is just bidding his time and waiting for Jassi to come to him. Such persistence is more effective than force or constant nagging.
He does not mind losing the small battles as his sights are set on winning the ultimate "war"😉.