Riki's invisibility doesn't usually kick in after you respawn. How can you activate it?
No longer necessary due to bug fix (Pointed out by Decency)
Usually you have to wait until you can attack something, blink at something, or TP.
The newest way I've discovered to do it is simply click your boots 3 times. This puts it back on agility or whatever you had it, but then allows you to go invisible.
Actually its just a visual bug, you're still invisible, you can check it by watching your Character's status (=Buffs) above your life and next to the hero's picture. Otherwise the best way to do it is to trigger it again, usually by attacking something or using an item (i suggest to change power thread status if you have them or use a tp scroll or a quelling blade)