"Wand" types of remotes are active only while a button is being pressed. This characteristic prolongs battery run time. If the remote generates the MUTE after a delay, the remote must be awake during that delay.

Regardless, there are a couple other considerations: First, I have not seen a TV with "Mute ON" and "Mute OFF" commands, there is only "Mute". As such, the remote cannot guarantee what will happen if a "Mute" command is issued. This is known as a "Toggle". Some TV's might come out of "Mute" if a "Volume Up" or "Volume Down" command is issued. If the remote supports "macros" you could brew up a guaranteed "Mute ON" with a "Volume Up" followed by "Mute" sequence, but this may actually bump the Volume up, before Mute.

Second, is there a guarantee that the remote will be pointed in the best direction after the 180 second timeout?

Pad/phones used as remote controls may offer macros, but you'll still need to manage the pad/phone sleep options.

Some of the higher end control systems could do this, but these generally require professional programming.

Out of curiosity, why do you want this function?