As the recorded stream of a channel is identical to the live... any inherent stream problems would (or should) be seen on both live and recorded instances of an identical stream.
Of course there are multiple sets of encoders, duplicated at two sites and an issue on one set of encode and mux may not be seen on another set of code and mux... So London C4 HD vs Newcastle can easily give different results in the event of a fault or setup issue. Even, potentially if a switch from one to another (coder, input stream, location, output stream to the transmitters) were to happen.
C4 HD on Sat is advert regionalised... not sure if that's true for Freeview HD (it is for SD, derived from the HD streams of course) but either way all (5/6?) incoming streams will be available within the Code & Mux centres for input to the relevant coder set that the OP will be watching...
So it is not such a simple question: Which Channel 4 HD version is this exhibiting a regular issue?
Then, such sound and vision issues are equally likely to be caused by other factors within any viewing location. High pressure propagation weather interference, electrical thermostat interference, mobile phone interference, for example, can all give varying and unpredictable issues. Only noticed on the most watched channel(s), of course.
BBC did have an issue with their kit many years back that gave rise to similar brief audio breaks - something to do with a large multiple of 2 (binary) frames and the Dolby E embedded audio signals and different brands / versions of kit en route to the coders from playout.
equipment at their end. Fingers crossed, no current problems, but clicks, pops and other noises (plus unconnected vision disturbances) have occurred on most U& channels irrespective of multiplex, Humax device and connection method.