Virgo tends to be a discriminating person that has good taste and high standards. Immediately, by becoming a person that isn't up to the Virgo standard will start to break up the relationship.
Virgo's do withstand a lot. In other words, this is going to take some time because a Virgo will overlook certain negativity since the Virgo is invested in a relationship. Virgo doesn't stay in a relationship unless he or she is invested in it.
However, let's say, you don't want to just come out and say, "I'm leaving", you can then become less careful in your appearance, more sloppy around the house, you can be more loose in your language, not behave as gentlemanly or as ladylike as a Virgo would like.
A Virgo also needs to feel that work and goals are important. If you stop caring or pretend that you have stopped caring and say, "Oh, it doesn't matter", "Oh, I don't care about this", "Oh, in the end, who cares", that attitude will quickly cool a Virgos artier.
In general, the Virgo needs of course, appreciation and a sense that you are in the relationship emotionally and intellectually and so any kind of withdrawal on that level will also drive a Virgo away.
Be very critical. That's a key to getting rid of a Virgo. Virgo's can be critical but you can't.