Does vaginal gas/queef/flatulence invalidate ablution? How should one handle the situation if it happens often?
Gas passed through the vagina (also known as queef) invalidates ablution. This is the opinion of Syafi’iyyah scholars as cited by Imam al-Nawawi.
“Anything that is excreted from the private parts of both men and women invalidates ablution. Regardless of whether it is in the form of faeces, pee, gas, worm, vomit, blood, stones and others. It isn’t different if it is excreted frequently or rarely ever happen usually. It is also isn’t different for gas passed through the frontal or back end of a man or woman’s private parts. This is stated by [Imam] al-Syafie rahimahullah in the book al-Umm and is agreed by the ashab [Syafi’iyyah scholars].” 
The Messenger PBUH said:
لَا وُضُوءَ إِلَّا مِنْ صَوْتٍ أَوْ رِيحٍ
“No ablution is necessary except when one makes a sound or breaks wind.” 
If it happens often due to the factor of an illness or debilitation, here, there is facilitation for her to still perform prayer although she passed gas through her vagina for it is considered the same as istihadah blood. Nonetheless, I advise those who are tested with this to perform the following:
- Try her best to wear or place something that could stop from passing gas;
- Hurry perform ablution when the time for prayer begins;
- Immediately perform prayer without postposing it for the duration of a person covering her awrah, listening to the adhan and iqamah, waiting for other congregants, determining the qibla, walking to the mosque and placing something to block someone from walking in front of her (sutrah).