I would be curious to hear about whether the pre-season is the best time to shop your aging stars as you rebuild... or, if a bigger haul can be found just prior to the trade deadline.
When do you think the best time of the season to auction off your core superstars?
Or, do you find that it is truly random?
Very curious,
JRNY

I'm not voting because I think the best time to trade them is based on a few factors.
If you are trading with a team that may be close to their payroll limit, I'd think pre-season would be best because they won't have the cash to chase a FA player.
If you are trading with a team trying to get over the hump and your guy is performing better than his ratings indicate, right before the deadline should be best.
And after the deadline may work well too because you only have one team you can trade him to and you'd be able to potentially increase your demands a bit.

After the deadline your likely return goes down, not up. The claiming team knows that if you want to move the guy, his team is your only option. Unless you luck into someone who's desperate enough to bid against himself, having 31 potential trade partners is better than having 1.

Following along the lines of the most potential trading partners line of thinking, I would say preseason. At that point you've got most of the league thinking they have a shot at competing and willing to bid for your players. At the trade deadline, all that is left are the teams that are actually competing, and more often than not, they are led by the more savvy owners.

The only time you're going to get value after the season starts is when you find a desperate owner.    He has all his chips in the pile and gets a devastating injury to a key player.  He has no one even vaguely capable in the minors and you're his last hope.

I know I'm not giving up much, regardless of how desperate I am, for a 34 y/o 3B rental. 

Sell before the season, buy during it.

Much thanks to everyone for adding to this thread. I doubt that my scrubs will be anyone's last hope. LOL. ;-P