As long as you supply the documents they are after they shouldn't stop your payments.
I'm self employed and didn't have all the paperwork they want to see (contract of employment, pay slips, time sheets etc) so I phoned them and was told to just send as much info as I could muster.
I have bombarded them with so much information on my 3 businesses that I'm hoping they are just too baffled to question it!
They have targets to work towards, so many cases they have to open etc, but as long as your claim is genuine you should be ok.
Would it be worth searching for a good rate credit card in case of emergencies in case they do suspend your payments for any reason? Just to take the panic out of the situation?
It is really daunting dealing with these people, HMRC, tax credits, council, all want to try and claw back whatever you're getting at the moment, but just make sure you send them as much supporting evidence of your circumstances as you can manage and I'm sure there's no need to panic.