Usually the stalling issue when stopping or slowing down is caused by issues with some of the plungers in the transmission front pump housing being worn out and sticking. The front pump and housing assembly will have to be replaced to permanently fix problem. It is a know issue with these transmissions.
If you choose to replace the front pump assembly, I would strongly recommend replacing the torque converter with a hemi or Suncoast unit and adding a Transgo kit while doing the repair...

Any good transmission shop can perform all of the above repairs....

_________________
Supporting Vendor and Moderator of LOST05 Jeep Liberty CRD Limited 
Ironman Springs/Bilstein/Shocks
Yeti StgIV Hot Tune
Week's BatteryTray
No FCV/EGR
Samcos/ProVent
SunCoast/Transgo
Carter Intank-pmp
2mic.Sec.Fuel Filter
Flowmaster/NO CAT
V6Airbox/noVH
GM11 Bld.fan/HDClutch
IronrockArms/wwdieselMount98 Dodge Cummins 24 Valve