DA means Decision Altitude. You must decide at that altitude whether you are going to go missed or continue the approach based on available cues. Since you are in a descent, your aircraft will dip below DA. Some aircraft actually touch down on the runway during a missed in Cat III ops. You should not be using this to cheat on an approach however. If you decide to go missed, go missed. Instability during a low approach has killed many a pilot.
AWACoff is correct. DA/DH is a decision altitude, as opposed to MDA, which is a minimum altitude. For the purposes of flying an approach in general, one may descend below decision altitude as it represents the altitude where the decision to continue the approach or abandon it must be made.
For the purposes of a checkride, in many cases the examiner may require that DA/DH represents a minimum altitude, and you must make our decision prior to that point to prevent descending below it during the missed approach. Clarify that with the checkpilot before allowing yourself below DH during the missed.
Obstacle protection is provided on the basis of executing the missed approach at DH/MAP with a subsequent climb gradient of 200'/nm, unless published otherwise. Accordingly, one should descend no farther during the missed than necessary. Initial obstacle clearance margins are minimal. Reasonable buffers are provided, however, these shouldn't be relied upon, and it is in the interest of safety to minimize any altitude loss when the decision to execute the missed proceedure is made.
14 CFR 91.175(c) provides the appropriate language: "no pilot may operate an aircraft...below the authorized MDA or continue an approach below the authorized DH...". This distinguishes between MDA (below which one may not operate) and DH. In the case of DH, one may not continue the approach, but no prohibition is made against descending below DH. If one descends below DH while executing the missed approach, one is clearly not continuing the approach. Therefore, descent below DH/DA is acceptable when executing a missed approach, but is not acceptable for the purposes of completing the approach.
There are those who will attempt to fudge the rules by stating that they began the missed approach and then had the runway in sight during the missed, so they landed. This is not kosher. Once below DH, continuing the approach is no longer an option if the required visual references were not met by DH. Further, if a missed approach is initiated, it should not be abandoned in favor of the runway (except possibly in an extreme situation such as a low fuel diversion or other inflight emergency).
In instrument checkrides, most examiners will bust you if you go below DH. They generally consider it an altitude that you use to go missed. I know many people who have busted for going 20 feet below DH while appyling power to go around.
I am a simulator PC and line check airman on the 757, and have experience as an examiner on many other 121 and 135 aircraft. Using the 757 for example, if the pilot makes his/her decision at DH(A) to execute the missed approach, the aircraft will always descend below DH(A) during the initial portion of the missed approach procedure. I do not expect pilots to make their decision at some point prior to this altitude to ensure never going below DH(A). MDA is another matter.