She passes wind continually; does this mean she cannot go to the mosque?

Firstly: 

Emission of wind invalidates wudoo’, because of the report
narrated by al-Bukhaari (135) from Abu Hurayrah (may Allah be pleased with
him), who said: The Messenger of Allah (blessings and peace of Allah be upon
him) said: “No prayer will be accepted from one who is in a state of minor
impurity until he does wudoo’.” A man from Hadramawt said: What is minor
impurity, O Abu Hurayrah? He said: Breaking wind silently or loudly. 

Breaking wind is of two types: 

1.

Where there is a time when it stops, such as if it was coming
out, then it stops for a while during which one can do wudoo’ and pray. In
this case, you have to do wudoo’ and pray during the time when it stops. 

2.

Where it is continual and there is no time when it stops,
rather it may come out at any time. In this case you should do wudoo’ for
every prayer after the time for that prayer begins, and pray the obligatory
prayer and whatever naafil prayers you want with this wudoo’, and whatever
wind comes out will not affect you, even if that is during prayer. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him)
said: 

If a person cannot remain in a state of purity for the length
of the prayer, he should do wudoo’ and pray, and it will not matter if
anything comes out of him during the prayer, and this wudoo’ will not be
invalidated by that, according to the consensus of the imams. The most he
has to do is do wudoo’ for each prayer. End quote from Majmoo’ al-Fataawa,
21/221. 

It says in Fataawa al-Lajnah al-Daa’imah (5/411): 

The basic principle is that emission of wind invalidates
wudoo’, but if it comes out of a person constantly, he has to do wudoo’ for
each prayer when he wants to pray, then if it comes out of him whilst he is
praying, it will not invalidate the prayer and he has to continue his prayer
until he completes it, as a concession from Allah to His slaves and so as to
relieve them of hardship, as Allah says (interpretation of the meaning): 

“Allaah intends for you ease”

[al-Baqarah 2:185] 

“and has not laid upon you in religion any hardship”

[al-Hajj 22:78]. 

End quote. 

Secondly: 

If what comes out has an unpleasant smell, it is not
permissible for you to go to the mosque, because of the annoyance that this
will cause to the worshippers and the angels. 

Al-Bukhaari (5452) and Muslim (564) narrated from Jaabir ibn
‘Abd-Allaah that the Messenger of Allaah (blessings and peace of Allah be
upon him) said: “Whoever eats garlic or onions, let him keep away from us,
or keep away from our mosque and stay in his house.” According to a version
narrated by Muslim: “Whoever eats onions or garlic or leeks, let him not
come near our mosque, for the angels are offended by the same things that
offend the sons of Adam.” 

Muslim (567) narrated that ‘Umar (may Allah be pleased with
him) said: O people, you eat two plants which I find to be nothing but
repugnant, this onion and garlic. I remember the Messenger of Allaah
(blessings and peace of Allah be upon him), if he noticed their smell coming
from a man in the mosque, he would issue orders that he taken out to
al-Baqee’. Whoever eats them, let him cook them to death.” 

This indicates that it is obligatory to keep the mosque free
of offensive odours and to prevent the one who has such an odour from coming
to the mosque or staying in it. 

It says in Kashshaaf al-Qinaa’ (2/365): It is Sunnah
to protect every mosque from all kinds of dirt, filth, mucus, nail clippings
and hair removed by clipping the moustache, shaving the head or plucking the
armpits, because the mosques were not built for that. It is also Sunnah to
protect it from offensive smells such as onion, garlic, leeks and similar
things, even if there is no one in the mosque, because the Prophet
(blessings and peace of Allah be upon him) said: “the angels are offended by
the same things that offend the sons of Adam.” (Narrated by Ibn Maajah); and
he said: “Whoever eats from these two plants, let him not come near our
place of prayer.” and according to another report: “…let him not come near
our mosques.” Narrated by al-Tirmidhi who said: It is hasan saheeh. 

If a person who has eaten that – i.e., one who has an
offensive smell of garlic and onions and the like – enters the mosque, it is
strongly recommended to remove him, so as to remove the offensive thing. 

By analogy, this also applies to one who passes wind from his
backside in the mosque, because that annoys others with the smell. So it is
Sunnah to protect the mosque from that and to make him leave for that
reason. End quote. 

But if the wind has no offensive smell, there is no reason
why you should not enter the mosque and sit there. Imam al-Bukhaari (may
Allah have mercy on him) said in his Saheeh: Chapter on breaking
wudoo’ whilst in the Mosque. 

Ibn Rajab (may Allah have mercy on him) said in Fath
al-Baari: 

What he (meaning al-Bukhaari) meant was that it is
permissible to deliberately break one’s wudoo’ (pass wind) in the mosque
because the Prophet (blessings and peace of Allah be upon him) mentioned it
and did not forbid it, rather he stated that it interrupts the prayer of the
angels. 

Al-Hasan, ‘Ata’ and Ishaaq stated that there is a concession
allowing deliberately breaking wudoo’ in the mosque. 

It was stated above that it is permissible to sleep in the
mosque in the case of necessity, and there is no difference of opinion on
this point. That includes the sleep of the person who is observing i’tikaaf,
because it is essential to the validity of his i’tikaaf, and it is also
permissible in cases other than cases of necessity according to the
majority, and it is most likely that one may pass wind whilst sleeping. So
if it were not allowed to pass wind in the mosque, it would not be allowed
to sleep in the mosque in any situation, but this is contrary to the texts
and to scholarly consensus. End quote. 

And Allah knows best.