doddering 

Definition:  (adjective) Infirm, feeble, and often senile.  
Synonyms:  gaga, senile  
Usage:  His mother was doddering and frail, so he hired aides to care for her around the clock.  

senile: behaving in a confused or strange way, and unable to remember things, because you are old

frail: (especially of an old person) physically weak and thin

around the clock: all day and all night without stopping