Well that is the whole point isn't it? Even your relationship building emails should have an element of sell to them. This doesn't mean you should bombard your loyal customers with gimmicks and free steak knives. It means you should never be afraid to ask them to do business with you again, and you should do so confidently.
Here are some ways you can increase the "sell" in your emails:
The first thing most people look at when checking their email is the "From" column. If they don’t know you, there’s a good chance the next button they click will be the delete button. There are three options that work:
1 The name of a person they know and trust (Account manager, sales rep etc)
2 A group they belong to ("XYZ Rewards Club", "ABC Frequent Flyers" etc)
3 A company they trust ("DEF Accountants", "ROI Investments" etc)
Once you have chosen which approach you will take, you should stick to it so your recipients can recognise your emails, and so you have a better chance of avoiding Spam filters.