One problem that could arise when storing very high resolution digital images?

The main problem is that storing very high resolution digital images take up a lot of space on a computer's internal hard-drive. It may be better to store onto an external hard drive or drives, DVDs, and so on.
Also, you must remember that should the digital images be 'very important' you must back-up and save to more than two external devices. And, at the moment, the data saved should be considered not very permanent as even the data on storage devices can deteriorate over a long time.