The answer you're looking for is probably a complex one. I'll have a go at it though.
One of the situations that trips the A/P to off is : TOGA button pressed when below 2000ft on the RadAlt. This means that the situation you describe will always take place during an approach.
I'm guessing that the design philisophy behind this is as follows. With two A/Ps engaged, the system knows that there is no discrepancy between the two systems and can therefore safely allow one of the A/Ps to fly the GA. With one A/P engaged there could theoretically be something wrong with the A/P that has not yet been detected. The system itself cannot figure this out by itself as the second A/P is switched off. So if you would allow the A/P to fly the GA you are setting yourself up for a possible flightpath deviation due to an A/P error, with no backup system except for the pilot!! Also below 2000ft there is no big margin of error should a pilot be slow to recognise the problem. Because of this the A/P trips off on pressing the TOGA button, leaving the pilot in charge of configuring the aircraft for a GA with the option of A/P engagement when climbing again through a certain altitude. Say you're pressing the TOGA button at 1600 ft, you could then safely engage the A/P again as soon as the aircraft is trimmed out again and climbing.
So the answer would be: no backup and no room to manouver in case of an A/P problem. That's just my guess though, someone else may be more knowledgable than me!