Hmm... I need to know where you set the obj1 variable...
Otherwise, this should work:
In the base, make a trigger:
Activation: east (if played east) present, set it to repeatedly
Text: basetrigger
Name: basetrigger
Condition: this
On Activation: inbase = true
On Deactivation: inbase = false
When the objective is finished, set the variable "objectivefinished" to "true"...
Make a third trigger to end the mission:
Text: endtrigger
Name: endtrigger
Type: End#1
Condition: inbase AND objectivefinished
That should do the trick!