Elected representatives responsibilities have been in question since the founding of America. The question is as old as the USA itself. When we elect someone does that mean he is to do our bidding or do we elect someone to do what he thinks is best?
The reality is somewhere between the two. No matter the issue, there will always be constituents that take an opposite position so it is not possible to represent everyone's view. On some issues, the constituents are dead wrong and do not have access to important information that their representative does have (secret documents, briefings etc.) Some constituent demands conflict with what is best for them.
Basically, a representative needs to use his best judgment, tempered by the input of his constituents and pressures of his party. However, if a candidate takes specific positions on specific issues during a campaign, it is perfectly reasonable to expect that on those issues and closely related issues, he will hold himself to the positions that got him elected.
In summary, we elect representatives to represent all of the people in his district. That includes those who did not support him. The only way to accomplish this goal is to do what he thinks is right. Our job as constituents is to let him know what we believe that to be. He will get his job review at the next election.
If your representative consistently takes positions you disagree with but still gets re-elected, then it is most likely the case that you are not of the majority opinion among your fellow constituents. You need to change your opinion or change enough other constituents' opinions to achieve your goals.