Recordings shouldn't just disappear. A number of 360 boxes received an over the air update earlier this week and this may caused the loss of recordings for yourself and some other forum members.
As japitts has indicated though it's usually due to a failing hard drive. Perform a factory reset via Settings > System > Factory Reset. You are given 2 options
Keep Recordings and Format Disk
Choose Keep Recordings, which means you won't lose your recordings, and any planned recordings, or series links you've set up. You may have to sign into your apps such as iPlayer, Prime, Netflix and ITVX again. Also Match frame rate and Standby power consumption may go back to their default settings if you have changed them.
Regarding having to keep signing into apps like iPlayer which keeps happening even though you disconnect everything over night. I find that I have to sign into most apps if I turn the 360 off either overnight, or reboot it during the day.
Turning off the box overnight means it can be slower to start up than normal as the box needs to check for any system and EPG updates.
Providing the box has been left on overnight then any system updates shouldn't mean having to log into apps again.