I've had this in the past, It did worsen for me to the point that the controller would never switch the machine on, and once I manually switched the 360 on the controller wouldn't sync witht the machine. I tried different 360 controllers but the same thing kept happening. In the end I just returned it to the shop.
had a similar problem to this - wouldn't turn on via the controller and also wouldn't connect to the controller if you turned it on manually.
It also needed to be turned on manually 2 or 3 times before it actually came on (ie the 1st couple of times you turn it on it would light up but not actually come on properly so picture on tv etc)
I took it back to Game who told me they had seen a lot of this recently and swapped it for a new one no problem.