If a political party abandons your core ideals, it would be time to distance yourself from said party. Better yet, try to avoid joining political parties at all. Political parties encourage group-think, and discourage individual thought and critical thinking. Think as an individual, not like whatever your current political group does.
Yes, I think a person should abandon their political party when it no longer sticks to that person's ideals. A political party is supposed to be based on certain beliefs and behaviors that traditionally do not change over time. Since our current political parties have drifted from their original intent, I think we should register our disapproval by abandoning them.
Of course, I do not think one party fits my ideals totally. That is why I would never claim to be Democrat or Republican. I have heard the green party is making a big push in some countries, but I am not sure what that party entails. I always claim myself as an Independent. If a party did not fit my beliefs for the most part, I would not belong to it.
A two party system is failing our country. A style of government formed of coalition groups would be more effective and less susceptible to gridlock in congress. People should be excited to leave their current parties and try out new ideologies and organizations. I think Socialist and nativist parties will spring from people who think the GOP isn't conservative enough or the Democrats aren't liberal enough.
When a political party does not match your views, beliefs and ideals, then you should no longer support it. Instead, seek out a party that better matches your viewpoint, or become independent if you are unable to find a party. Staying true to yourself is more important than sticking with a political party.