You may want to check with Williamson, My guess would be the battery is not holding charge as well as it once would have. A 7 year old battery will have a lot of crystalization around the lead cells. If the control is similar to our units they need a minimum of 9V to remained powered up.
As you shut the tap and stop flow the Pump will increase both pressure and try to draw more current from the battery This increased load may pull the battery briefly below 9V causing the control to power down. Once the battery is no longer under load volts will recover slightly.
If you can measure the voltage at the battery and controller leads as this occurs. Worn faulty and or rusted connectors can also cause volts to drop along the cable length so check and replace those that are in bad condition. Poor or worn terminal connections mat be another cause.
In particular check the Negative (Ground) connection to the battery terminal
You do not mention what rating the fuse is, Or what flow setting you run on. The Varistream i believe has a 1 - 9 setting. Also what calibration setting do you have I believe the default setting is C.
Another possibility is that at 5 years old some of the components in the controller are worn and less able to cope with changes in current draw as load from the battery changes.
The suggestion would be to consider replacing the battery once you have eliminated and poor electrical connections.