on the dead run?

"...Usually well balanced except when on the dead run."
(from http://www.us-squash.org/rbl.html)

What does "dead" mean here?

Or, what does "on the dead run" mean?

Probably means the player is well balanced except when exerting himself to the maximum.

But if running is possible in Squash then I guess it could mean when running as fast as possible.

In tennis, hitting the ball on a "dead run" is when you are forced to instinctively return a shot in an ill-prepared and less than optimal position, usually due to your opponent volleying a fast one to a point on the court that you least expected.

"Dead run" is also a term used in sailing; meaning to sail against the wind.