A Picaxe only uses polled interrupts, i.e. they occur when the firmware goes looking for them. They aren't the same as the interrupts that you might use in a raw PIC programmed in "C".
They can be set to occur on pin conditions, or in the case of X2 parts, flag conditions. If you set an interrupt to occur when a particular condition (pin or flag) exists, then you either have to wait for it to go away or clear it directly, if you don't want to be in a loop of continuous interrupts. Given that the interrupts must be cleared in order to prevent such loops, you then naturally have to re-enable them when exiting the ISR.
First you use hintsetup to make it known what hardware conditions are to set flags
Then use setintflags to cause the picaxe to respond to the conditions
If a flag is set by the hardware and used to trigger an interrupt then you must clear that flag before proceeding (by setting it to zero). Otherwise you just get another interrupt.
It is all in the manual but needs careful reading and maybe some experimenting.