Is there an AM0805 register setting that affects the oscillator allowance of the 32 kHz crystal? For example, how about Bit 7 (STOP) of the Control1 Register?
Bit 7 (STOP) of the AM0805 Control1 Register does not impact crystal oscillation in any way, and does not even start/stop the 32KHz clock. It only controls the clock tree generated from the 32 KHz clock, and is used for synchronization purposes. There are no special registers for oscillator allowance. The most likely cause of reduced oscillator allowance is hardware design. Confirm that your layout follows all of the Layout Guidelines in section 3 of the AM08xx/AM18xx HW Design App Note (posted here), especially the solid ground plane under the RTC and crystal. If there is no ground plane under the RTC and crystal, and especially if there are signal lines routed under the crystal and RTC, then oscillator allowance will be reduced.