Praise be to Allah.
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.
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.