I don't think a closed-inactive account is going to be a specific negative mark, it's just not "open" giving you a lower utilization ratio. And any past due amounts on those accounts would show up whether it was still open or not.
I don't know any specific rule about credit lines. I've never had an account closed for inactivity; currently my credit report shows a car repair shop card that is two years old that only works in a state I don't live in anymore, and joint JCPenney card with my ex-wife that neither of us has used in 10 years. I guess it depends on your level of risk, and the individual lender. If you have presented a risk in the past, the lender may want to limit their exposure to future risk by closing your line once you get caught up.
I can only suggest to spread your purchases around several accounts, but only if they are zero annual fee and you pay the balances in full every month.
