Is there a statute of limitations on student loans whereby the government just writes them off after a period of years and the student's credit is not affected?

Sorry, no statue of limitations on student loan debt; it helps at the time but is not free. Government does not write anything off, they will collect no matter what, so be prepared to have to pay, which is only fair. It is almost an interest free loan, you were honoured in being able to get it. If you don't pay, then all of us in Canada pay the price for default.

Your credit report will be effected until the debt is gone.