"Continuous support" implies uninterrupted service, not necessarily by choice. Ex: Web hosting companies are expected to provide continuous support to their clients 24/7. {They are expected to respond to clients at any time of the day, any day of the week} In this sentence, you would use"continued support", which suggests that the person "chooses" to keep supporting, so you are thanking him/her for his/her choice. Ex: "Thank you for your continued support of this charity organization. Your donations help a great number of people in need."