Very good question. This sound like an issue that has placed a lot of strain on your relationship. I hope my answer helps you understand some of the possible problems and gives you some ideas on how to solve them.
Some people who are very emotionally labile and have wild mood swings are also very depressed.
Depression itself can cause the symptoms and is the most common psychiatric disease that is responsible for being deeply saddened by everyday things. Luckily, it is very treatable.
There are personality disorders in which people are very emotionally labile. One example is Histrionic personality disorder. People with this disorder frequently cry or laugh during times when the situation is neither sad enough or funny enough for that type of reaction. Sometimes these personality traits are rooted in how the person was raised and have more to do with the emotional instability of the parents.
I suggest that you encourage your girlfriend to schedule an appointment with her
primary care physician. He or she may pick up on this issue and recommend that she talk to a board certified
psychiatrist. This doesn't mean that she will go. She will have to recognize her emotions as a problem in her everyday life in order to want to seek out help. Good luck.