Trouble Maintaining a Good Fire

Q. I'm having problems maintaining a good fire. It stays burning if I leave the door cracked open slightly. As soon as I close the door it dies out! Also each time I open the door to add a piece of wood it back drafts big time! I removed the cap from the chimney and this has allowed me to now close the door and maintain a decent fire, however I still have the issue with back drafts each time I open the door! I'm wondering if I may possibly need to extend my chimney height? This is a new woodstove insert along with a new stainless steel liner recently installed.
 3-2-10 rule

3-2-10 rule

A. Assuming the liner is the correct size and has been installed properly, the chimney height may be an issue. The rule of thumb for chimney height in relation to home/roof, is called the 3-2-10 rule. The rule states that chimney must terminate at least 3' above the roof line, where the chimney passes through the roof, and 2' above anything within 10' that is combustible, i.e. asphalt shingles, wood Soffits, etc. So if the chimney does not meet these requirements it can reduce the draw that the chimney can have. Adjacent structures and foliage may be contributing to the problem as well. If there are very tall trees or homes surrounding the chimney, that can reduce air flow. Another issue may be the path of the prevailing winds around the home which may be blocked by any of the above mentioned possibilities.

Soffits: the underside of a structure like overhanging eaves.