By breath disappearing, do you mean the breath stops (for a very long time) in one of the pauses between exhalation and inhalation?
Or do you mean the breath becomes increasingly shallow and then finally stops? (Or both?)
It's more that the breath can become increasingly subtle not that breathing stops or becomes shallow (usually the breath is pretty deep but very slow when it's like this). So even when counting breaths it can appear to disappear - but actually that doesn't usually happen during breath counting meditation because of the focus. When breath watching without counting and other kinds of meditation it can happen that the breath appears to disappear and if your attention has been on an object of meditation other than the breath you might even wonder suddenly when the last time you took a breath was.
And the result would be the meditation is broken because of gasping for air?
Not usually but it can happen - I did gasp once during a Zen sesshin and probably my breath had gotten super low. During Zen sesshin you can get into very deep meditative states and the breath can totally appear to disappear (people talk about this and Zen teachers talk about it but Master Sheng Yen wrote about some of the things that can happen during deep meditation). Generally this means that you've gone too deeply into a meditative state but if your concentration gets that good regularly then you can use it as a scalpel depending on what kind of meditation you are doing. This is much less likely to happen during Vajrayana practice because generally the sadhana is always changing although it might happen when resting non-conceptually for a long time or if you focused on parts of a deity visualization for a long time. I don't know if the Vipassana people experience this because I never did a long vipassana retreat but Theravadin monks have noted it too.
_________________Kirt's Tibetan Translation Notes
"Only you can make your mind beautiful."
HH Chetsang Rinpoche