So hope your dad's doctor can help get his symptoms under better control. I think if the infections are returning within days of finishing the course of AB, it suggests the infection is still active, your Dad should be going straight back to see the doc or having the doc visit him at home. A sputum sample analysis if not already done will help to determine which AB is going to help clear this, but its down to the doctor to help keep on top of this with your Dad's cooperation. Keep communicating and returning to see the doc if things are not settling down.
If your Dad is mostly housebound there should be contact available to you with the Community Matron who will visit your Dad at home. If your Dad is not having home visits by the ~CM or a respiratory nurse, contact the GP and ask for this.
Do hope you can get some better care for your Dad put into place.
On Monday I would suggest contacting the BLF helpline for further advice on this situation (click red balloon top right) Helpline is manned 10am to 5pm normal working week days.
Hope your Dad is soon feeling much better.
Best wishes BC