Why Doesn't Out Red Eared Slider Bask?

Don't worry about it. I've had this type of turtle before. They don't bask as much as other turtles and prefer to hide in the water. 
 
He'll be fine, just leave the option open for him to bask. He knows if he needs it and he won't let his own shell get soft.
Also, it's possible that he doesn't want to bask while you're around. He may be basking still. Mine always sat up on his little turtle dock and as soon as anyone entered the room he'd make a dive for the water. Maybe yours is similar.

#1: Absolutely DO NOT cool his water. If you do this, he could get into the deathzone, which is the temperature where it is too cold to stay awake but too hot to go into hibernation. I suggest giving him a few more weeks, and if he still doesn't consult a vet.