Unfortunately the answer is NO. If a recording is deleted by a user, or because the Series Manager is set to only keep a certain number of episodes, it is kept in the Recent Deletes folder (like a computer's recycle bin) until it is overwritten by another recording. In this case you could just go to that folder, select the recording and restore it. But when it is deleted by the DVR to create enough hard drive space to record a new program, the deleted program is immediately overwritten and can no longer be recovered.
Here are your options to prevent this from happening in the future:
Protect your recordings by selecting the Save Until I Delete option. A shield symbol with a plus sign will appear beside each protected recording. This program cannot be deleted except by the user or the Series Manager. Just be aware that while you won't lose these recordings, when you run out of space the new recordings will stop.
Unprotect less important recordings so that they can be overwritten if necessary.
Record more shows in SD rather than HD. HD takes up about 4 times as much disk space making it more likely for you to run out sooner. If you don't need the wide-screen or quality, consider this option.
Schedule fewer recordings.
If you don't already have a 500GB model, upgrade your DVR. But you won't be able to take your recordings with you, so you'll have to watch them all before the exchange.
If you have any DVR model other than a 2708 or 6416, you can expand your recording space with an external hard drive.
As for the recordings you are missing now, you can try searching for them in the On Demand menus, or going online to sites such as Hulu or the individual network sites, or there are pay services such as Netflix.
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