"Thank you for your continued support" is the standard. You're thanking someone for what they have done (with a slight suggestion that it would be nice if they continued. Continuous suggests they supported you every step of the way, which is seldom true. Continuing suggests they're going to keep supporting you, but you don't really know that – they may change their minds. They seem to mean basically the same in the dictionary. However, there is a popular belief in the English teaching in my country that they mean differently. For example, After a cup of coffee, I continued to do my homework. (I was doing another thing but not my homework before drinking the... For an epitaph, would you write: Her joy and love of life continue to inspire us all or Her joy and love of life continues to inspire us all TIA A discussion arose about whether one could substitute ongoing availability with continuing availability and what the difference would be, if any. Actually, my gut feeling told me it should've been
