here the best translation of the verb i can think of, is "become", it also indicates "something in progress", or "get" in the two meanings above.
जैसे जैसे समय बीतता है पत्नी पुरानी होती जाती
as time passes wife gets older(wife 'goes' through the process of getting old)
जैसे जैसे समय बीतेगा, जीत की यादें पुरानी होती जाएंगी
as time will pass(or time passes), the memories of victory will become/'go through the process of becoming'/ be/get outdated.
it is simple, it is 'happening' also and 'going' (i.e., it is in motion/progression) as well. (it 'goes' something 'happens'= becomes)
if i say hoti hai or hongi then it is a declaration. like 'sun is warm'
ho jana may also indicate occurance
ye apane aap ho jaata hai ये अपने आप हो जाता है
it happens automatically
but hota jata hai(होता जाता है) in above sentence will tell u that repeated action is being performed