Sometimes - adverb of frequency For example: I sometimes go to the beach. Sometime - at some point but exact time is unknown For example: I'm going to go for a swim sometime tomorrow.

"Sometimes" doesn't have a fixed duration and refers to multiple occurrences, and is for that reason used in the plural. "Next summer" in this sentence has ascribed a specific breadth of time for the visit, and so the 'visit' has a singular 'time' during which it will happen, and is therefore in the singular. For "sometimes" to be correct, you would simply knock off the "next summer" part of the sentence and you'd get "I do hope you will be able to visit our school sometimes".