The plant is still there and can process them but the demand has evaporated. The reason: Del Monte was fucking stupid.
Peaches are climacteric. When they ripen they naturally produce the plant hormone ethylene. This triggers a complex ripening process where aromas and volatiles are produced (aka flavor). It also causes rapid softening of the fruit and makes canning them much more difficult.
So what are clingstone peaches. These are peach varieties that have been selected for the down regulation of ethylene production and response. They are hard, sweet, but mostly flavorless, and do not separate from the seed (stone). They ship and process well because of their firmness but taste like shit.
So Del Monte produced good looking but shitty tasting product (extra tin can flavor) and the demand dried up over the years.
Why? Did this happen and why did they go bankrupt? They were allowed to become a regional monopoly.