Starter Motor

Hi all
I have just been told the reason my battery is not holding much of a charge, even though the battery is new, is because my starter motor is drawing too much from the battery on starting. I have the battery at full volts, it sits on an optimate yet 4 days in my cold UK garage in winter I go to start it, it turns twice and does not fire the bike. Jump start it run it for 5 mins, bike charges the battery, bike then fires, turn off, fires turn off, fires from the same battery. Should i be looking at a new/reconditioned/ebay starter motor for my beloved Sprint ST 1050 2006

 

Thank you for a prompt reply, I will do just that, I am in the UK so when you say refresh, do you mean a Rebuild Kit