It would be much better stated as "to influence power, you must give feedback". And the only forms of feedback you have are your vote, and your election efforts (campaign contributions, time, etc.).
As long as a candidate or party is "going in the right direction", your feedback should encourage them. When they start going in the wrong direction, it must discourage them (through the withdrawal of your vote and support).
Otherwise, your vote and campaign support means nothing. It gives no feedback - they get it whether they deserve it or not. They can then adapt their behavior to those who will withhold their votes, because they are not going to lose you.
I and lots of others on this board maintain that this is exactly what's been happening. So many conservatives have decided that it's "my GOP, right or wrong" that the candidates know they can count on the votes and support of conservatives, no matter what they do. They can increase government handouts, grow the bureaucracy, put us deeper in debt, and so what? Their refrain about the conservatives is "where are they going to go?" So the conservative viewpoint can be safely ignored.
The mainstream Republicans will keep going in that direction (appeasing moderates) until some sort of feedback pulls them back. After all, not one in a hundred Republican politicians has any deep philosophical conviction about conservative principles. (If they had any when they got elected, it probably got beaten out of them by the political establishment.) They just go where the votes are.
Consider them a "vote optimizing machine". They do whatever strategy maximizes votes, regardless of whether that strategy is conservative, or even Constitutional. If they can count on certain votes no matter what, then they will inevitably ignore those votes, and seek out more votes by appeasing groups whose behavior they can influence with government giveaways or whatever. It's not that they don't like you - they are simply indifferent to where the votes come from. Since you are giving yours for free, they'll take 'em - and then go looking for more somewhere else. Only if you make them pay a price for your votes will you influence their behavior. And that means you must be prepared to withhold your vote if their behavior is not acceptable. And that means, unfortunately, that you must be prepared to lose in the short term to maintain your long term influence.