I feel like I can answer this because I am similar to your girlfriend – I take the pills for that long and am generally somewhat similar in a lower libido and affection level, as well as being very affectionate while not taking the pills.
I think the mature way to approach this is to think of it as a couple’s dilemma. You two obviously don’t want babies, that is the goal in this situation. She has tried the pills and they have a negative effect on the relationship. There are more methods of birth control that both she and you can try. To reduce the sensitivity of this issue you can make it clear that you are willing to put forth effort, such as wearing condoms, or getting a vasectomy if you really don’t think you ever want children, or to simply support her needs, such as accompanying her to the doctor’s office or picking up her prescription, if that’s what she desires.
If this is something she is willing to put effort towards fixing, she can talk to her doctor about alternatives such as the NuvaRing (a plastic ring that stays in her vagina even while having sex, stays in for 3 weeks then comes out, similar in functionality (hormonally) to traditional birth control pills), or the depo-provera shot done each three months. She can also talk about the option of having an inter-uterine device put in – this is a longer term solution and may not be recommended as a casual method of birth control. There are also lower hormonal pills which may cause the negative effects to dissipate.
Basically, you just have to approach this with tact and grace, and make it clear that it’s not something you blame her for, and that it’s something you’d like to work on, if she’s willing to do so. She can go talk to a doctor for more information. You shouldn’t try to “prove” it’s the birth control, you should simply state your concerns and your thoughts that it may be the birth control. Your emotions are enough proof at this stage. More proof either supporting or disproving your birth control theory can be gained if she decides to switch for a bit.