Basically, you have three options:
The camera doesn't record a thing. It instead immediately uploads it (through a secure channel) to your military base, and the recording is mad serverside.
If anyone manages to steal the camera, he will just steal a nice satellite/3g connected camera with a send-only apparatus. While this might be useful to reverse-engineer the technology used, your enemy will have no footage of your operations whatsoever.
The live feed can also be used by commanders to make last-minute decisions and have a tactical advantage.
If the enemy produces a jamming signal strong enough, you will have no records of the camera. This can be also used as a decisive hit to your intel capabilities, if your generals are using the live feed to take decisions in real time.
The signal could also be used by a technology advanced enemy to triangulate your soldiers' position. (thanks Agent_L)
The camera records everything, and all is encrypted on disk, using a system like Bitlocker or similar. The recording can then be reviewed safely at the base.
All footage can be recorded in high quality, regardless of available bandwidth or connection loss.
The enemy may be able to capture your soldiers and force them not to disable the camera, so they would (theoretically) be able to retrieve the non-encrypted datas still stored in memory. With modern cryptography techniques, this could amount to a few minutes, seconds, or even a few frames of recording, so the advantage of this for the enemy may vary (thanks MichaelK, André Paramés).
Internal storage size will also limit the quality/recording time of the camera. This becomes important for older (less space) camera models or very high resolution cameras (thanks Taegost).
This is the system I would use. It involves a bit of both, and consists into recording everything, uploading all the recorded data to the base, then deleting all data already sent.
No quality loss, recording will take place regardless of signal, basically the advantages of both approaches combined
If the enemy jams the signal for long enough, you will fall back to the "Recording" case, as data never gets uploaded to the server.