Time stamps are also signatures; see for instance RFC 3161 which is the most commonly used time stamp format. In particular, such time stamps also rely on certificates (the TSA certificate), and thus also expire.
So you need regular time stamping; whenever the latest time stamp is about to expire (but before expiration), you need to obtain a new time stamp computed over the previous time stamp. Such chaining is described in several standards, including PAdES (which supports embedding signatures and time stamps within the PDF file itself); a somewhat clearer description of time stamp chaining is Evidence Record Syntax.
To survive unexpected loss of a TSA before the time stamp expiration date (e.g. due to a compromise), you can use several TSA and interleave them in the chain: you get a time stamp from TSA A, and immediately after another time stamp from TSA B (computer over the time stamp from A). Whenever either time stamp is about to expire, expand the chain with two extra time stamps, again from A then from B. With interleaving, you can survive the loss of either TSA (but, of course, not of both).