Is Local Housing Allowance affected by quitting of income based job-seekers allowance?

basically im fed up of being caught in the JSA system, when i have a part time job that pays about the same as JSA, and where they ignore my first �5 earnings, i only get a fiver a fortnight off them anyway, which i could survive without. i dont want to be sent on the TNG course again as next time round ive been told itll be for 3 years rather than 13 weeks, and TNG is not helpful for me. if i quit JSA, how will this affect my LHA, if at all?