Firstly, do you accept that you have missed a month (or more)? It is your responsibility to make the monthly payments, so writing it on a calendar would be a better way to remind yourself, rather than waiting for the letter. "Not remembering" isn't a good enough excuse if you have to make a monthly payment.
However, if you have missed one, go now and pay it - and explain your circumstances, ask to speak to a manager and ask for the circumstances to be taken into consideration. I can't promise it will work, but it's worth a try. If no, go to your bank and ask for a short-term loan for a couple of months - you can then use the payments you would have paid to the council, to pay it off before the end of the financial year.
I am sure they receive many such "excuses" - I am not saying that yours is not a genuine mistake, I am sure it is - but there has to be one rule for everyone.