All depends what the contract says. As a general rule, there would be nothing illegal about the contract saying that you are only paid for 10 months of the year if you only work 10 months of the year. "Term time" contracts exist in many public sector jobs. If money management is an issue, can she request that her salary be paid in 12 monthly installments instead of 10?
Was she paid over 12 months before being offered the new contract? Is it the same job? What reasons was she given for being on successive contracts e.g. filling in for Maternity leave, career break etc. May be some fixed term working act implications here.