Will my Service Provider’s SAS 70 report expire and does it need to be renewed?

Not really. The report targets auditing of either one point in time (Type I) or a specific time period (Type II) such as a 6 month period of auditing. Therefore a report is valid as long as it was correctly produced. Of course things change and companies procedures and policies and their ability to execute them will change over time as well, so realistically a report is of less and less value the older it is. Any given provider will probably want to–or be required by their customers–to have a new report generated on a yearly basis as it seems reasonable to ensure that policies are up-to-date and followed appropriately.