I'd like to second David Schwarze's advice to not drain a lead acid
battery more than 80-75% full charge. Addition to thicker plates, a deep
cycle battery should also have more clearance beneath the plates to allow
a greater amount of lead sulfate (I think its lead sulfate) to accumulate
before it bridges the plates. Lead sulfate is part of the charge storage
mechanism, but some of it "drops out of" the reversible reaction,
especially if you deep discharge the battery.

My apologies to any electrochemists that read this:)

Alistair