I just started working on a contract basis for a Canadian company. The contract is for 1 year. I live in the US and am working remotely. I will need to travel to Canada 3-4 times during this year (2-3 weeks each visit) for business activities, including giving training. Will a work permit be required? If so, do I have to apply for a work permit each time I come to Canada? Thanks for your opinion.

Yes, a work permit is required, and a Labour Market Opinion may be a requirement for that. You could seek a one year work permit to cover the multiple trips or seek individual work permits for each trip. There are advantages and disadvantages to either approach and the better choice would need more detail.