This might be two separate problems.
If I remember correctly, by default the 5000T automatically goes into standby after 4 hours if you don't press any keys on the remote (or the top of the box). If you don't want this goto menu/settings/system settings/power management and set automatic power down to off.
If your 5000T is anything like mine it crashes (when in standby) almost daily. The Humax fails to respond to the remote in a timely way. Eventually it goes through the boot procedure and turns itself off again. At some point no LEDs are lit. Pulling the plug is quicker, but I'm wary of doing this too often because it might damage the disk or corrupt the contents. Usually this has happened the first power up of the day, but it has happened at other times. I used to use a power timer to switch the machine on early (04:30 I think) and leave it on all day. That seemed to vastly reduce the problem. What with the number of rescans required in the last year or so (which cancel the power on timer) and power prices I no longer do this - and the "not responding" has returned.