I have noticed that if the TinyTV2 has been off for a while, the TinyTV2 will not turn on with the remote.  I have to push the button on the top of the TinyTV2 to power it on.  Afterwards, the remote can be used to turn it off and even back on again.  It seems that if the TinyTV2 sits for some time the remote will not work for powering on.

Yeah this is normal... the settings.txt file has a powerOffSecs parameter that is defaulted to 300 seconds.