Fridge/freezer gets cold, but won't stay cold.

Question

Our Fridge Freezer stops working once it has reached the correct temperature. The internal lights work, but it will not begin cooling again unless it is turned off at the wall briefly and then turned back on.

 

It has a digital thermostat with 5 lights at the top, but adjusting the setting on this doesn't seem to help.

 

Is this likely to be something I can fix?