If a connection remains idle long enough for the timestamp clock of the other TCP to wrap its sign bit, then the value saved in TS.Recent will become too old; as a result, the PAWS mechanism will cause all subsequent segments to be rejected, freezing the connection (until the timestamp clock wraps its sign bit again).
With the chosen range of timestamp clock frequencies (1 sec to 1 ms), the time to wrap the sign bit will be between 24.8 days and 24800 days. A TCP connection that is idle for more than 24 days and then comes to life is exceedingly unusual. However, it is undesirable in principle to place any limitation on TCP connection lifetimes.
We therefore require that an implementation of PAWS include a mechanism to "invalidate" the TS.Recent value when a connection is idle for more than 24 days. (An alternative solution to the problem of outdated timestamps would be to send keepalive segments at a very low rate, but still more often than the wrap-around time for timestamps, e.g., once a day. This would impose negligible overhead. However, the TCP specification has never included keepalives, so the solution based upon invalidation was chosen.)
Note that a TCP does not know the frequency, and therefore, the wraparound time, of the other TCP, so it must assume the worst. The validity of TS.Recent needs to be checked only if the basic PAWS timestamp check fails, i.e., only if SEG.TSval < TS.Recent. If TS.Recent is found to be invalid, then the segment is accepted, regardless of the failure of the timestamp check, and rule R3 updates TS.Recent with the TSval from the new segment.
To detect how long the connection has been idle, the TCP may update a clock or timestamp value associated with the connection whenever TS.Recent is updated, for example. The details will be implementation-dependent.