Just to clarify a couple of points:
1./ Surges referred to are in all likelhood voltage surges or spikes NOT power surges NOT current surges.
2./ Interesting to note that a surge bar has helped, further reinforcing pt. 1. However if the protective devices in the surge bar (called MOVs or metal oxide varistors) are conducting regularly, they may eventually burn out - which puts you back to square 1 - please see pt 3./
3./ Getting to the bottom of where/how these voltage spiles or surges are originating is difficult. Depnding upon the time constant (how fast or low the spike is with respect to time) a digital or analogue meter will not help. It may require specialized test gear such as an oscilloscope
As one owner sugggested, try an outlet on another boat, if there still is a problem suggests a general marina problem or at least in that area of the marina
4./ Curious whether or not your shore power runs through via the inverter to the AC outlets - beleive this is standard ABYC practise. Inverters can be noisy. This noise may be upsetting the IPAD charger.
Can you take a separate cheap dc to ac inverter block and connect directly to the ships battery to see if the problem still persists?
With respect to Anne, advice on a volt meter. These are good to have on board . Suggest an inexpensive digital one say less than $100. I have been looking a an inexpensive Sears one. Its a clamp on, which means it can safely measure dc current safely. But as a bonus, it can also measure AC currrent (these tend to be much more expensive).
PLEASE TO ALL BE SAFE !!! when neasuring ac and dc quantities. If you are not completely sure ask one of the Ranger owners who are quite familuar with these measurements. Contrary to to belief dc or 12V battery systems can be dangerous too under the right circumstances. Accidentally briding a metal watch band across +ive and -ive DC terminals resulting in welding your watch to these connections - a permanent handshake.
Regards, Frank "Blue Horizons"