Ruling on one who is excused from fasting having intercourse during the day in Ramadan

If both spouses are excused from
fasting during Ramadan, such as if they are travelling or they are sick with
an illness that makes it permissible not to fast, in this case it is
permissible for them to have intercourse during the day in Ramadan, without
needing to offer expiation. 

Ash-Shiraazi (may Allah have
mercy on him) said: If he breaks the fast by having intercourse when he is
sick or travelling, no expiation is required, because it is permissible for
him not to fast, so no expiation is required when it is permissible not to
fast.

End quote from al-Muhadhdhab
(6/373) 

Shaykh ‘Abd al-‘Azeez (may Allah
have mercy on him) said in Majmoo‘ Fataawa Shaykh Ibn Baaz (15/307):

If the one who has intercourse
during the day in Ramadan is travelling or is sick with an illness that
makes it permissible for him not to fast, then no expiation is required of
him, and there is no blame on him, but he has to make up the day on which he
had intercourse, because it is permissible for one who is sick or travelling
to not fast, by having intercourse or otherwise.

End quote 

In a case such as yours, where
there is chronic sickness, you may refrain from fasting and feed one poor
person for each day. 

And Allah knows best.