This is a topic that interests me too, although I do think it has been discussed quite a bit in the regular forum earlier in the year because there was a guest Blog post by a forum member on budgeting for wardrobe/fashion.
I don't exactly work part-time, but I do contract work. I'm often working more than 40 hours a week, but then have gaps between contracts. Depending on the year, I guess it works out on average to less-than full-time and it definitely affects my budget.
I don't have a huge problem putting money away, so much as justifying "spending it on myself" or on clothing/grooming when I fear I am going to need it for something else in the future (i.e. being in deficit between jobs) or could spend it on something else (rarely get to travel for enjoyment, dinner or activity with the SO or friends, gifts, paying of medical bills, education, savings, hobbies).
Not saying that this is the case for you, but I often see friends who work part time or make less than their partners taking basics like haircuts and replenishing tee shirts out of their own money or their "fun budget" while the hubby wouldn't dream of spending his fun money on haircuts and pays for those out of the household budget.
One way I deal with overcoming this is to have friends and family give me giftcards for haircuts, beauty supply stores I frequent, and my favorite stores for holidays, ect. That way the money is earmarked.