"A period of service shall be deemed to be continuous" It could say, as Gen Rugg said, "to have been". That would have made more sense. Another alternative would be "shall be deemed continuous". I believe this is incorrect grammar, but to me, the meaning is clear. I am assuming this is a legal contract. It reads like one. Legal contracts can be a problem because there are many ways smart lawyers will try to interpret them. Because legal contracts can be a problem due to people pushing the limits of interpretation, sometimes lawyers will put in language that is not necessarily grammatically correct, but still understandable to get the point across.

"to have been..." would have made more sense.