Mrs Glum
There has been some concern among easyJet managers that pilots on part-time contracts will not be as 'sharp' as they should be due to lack of practice! To that end they have built into the contract the facility to get you back full-time if you start messing up. It is no more sinister than that as far as I can see.
Other companies (GB Airways is one but I am sure there are others) offer much better part-time deals involving a 'job-share' scheme. Basically, you do a full roster but shared between 2 pilots with one pilot always doing the first half of the month and the other always doing the second half. Even then they usually demand that after a type change (such as 737 to Airbus) you must work full time for 6 months to 'get your eye in'. Hope that helps.