Support is one of the best marketing strategies around.
You should see your customers as ambassadors. Most people tend to recommend things they had good experience with. No matter if this are cool spots for spending a weekend, great wine, time saving software or anything else.
If one of your customers who has a problem or a question is contacting you for help this is a perfect opportunity to shine. Much better than annoying random people with marketing mails or cold calls.
Offering a helping and timely response will often remind your customer how great and useful your product is. Which can lead to the one or other recommendation. As we all know: Word of mouth is the best marketing.