pH meters and Dissolved Oxygen meter sensors are the main products that requrie maintenance, although it's worth pointing out that for all battery powered products, it is worth taking the batteries out before putting the meter away for long periods of storage.
For pH meters it is the electrode that needs to be kept maintained in order to pro-long the working life of the system. If you have a pocket tester then it is just the electrode end that needs keeping wet - not the whole instrument! Generally, it is best to store the electrode wet, which could be in tap water or buffer solution - but not in dionised or distrilled water as this will discharge the electrode glass measuring membrane and make the electrode slow to respond when you next use it.
If your pH meter won't calibrate with an electrode that hasn't been used for a period of time, then try soaking the electrode in pH 4 buffer solution and leave overnight. Then try calibrating it the next day, this can often 'wake' the electrode back up and it will perform as before.
With Dissolved Oxygen meters it is important that the membrane at the tip of the sensor is not only intact, but also clean and free from scratches and pin holes. In addition the internal area of the sensor should contain the required amount of solution otherwise the sensor will not perform properly or at all.