[Tim Hancock]

I doubt this will help, but I have sucessfully repaired some plastic motorcycle body parts by welding the cracks on the back side of them with a soldering iron. Basically you hold the tip on the back side of the crack and dap the plastic around as it melts. This has worked long term for me on "non-stressed" body parts that had been damaged by a mishap, but simply welding the surface of a crack is not going to cut it in your situation as you need full penetration on the relatively thick seat cross section to develop sufficient strength.

If the plastic your chair is made of is "weldable" like my motorcycle parts, you may be able to "v" groove the crack and then carefully melt in some additional filler plastic making sure to start deep in the groove. You would need to cut somedonor plastic away from some other un noticable place on the chair to use as the filler.