Below is the sample data and the props.conf that I used. When Splunk indexed the data, it only got 12 hours.
6:44:04 AM, Source = GetCookies, xxxxx....
6:44:05 AM, Source = IsFirstTimeUser, xxxxxx....
3:52:49 PM, Source = GetUserDetails - API,xxxxx....
3:52:52 PM, Source = GetCookies, xxxxx.....
And the props.conf that I used to parse the time.
[my_source_type]
TIME_PREFIX=^
TIME_FORMAT=%H:%M:%S %p
Your props.conf is not correct.
TIME_FORMAT has "%H" which is the 24-hour-clock hour. Because %H explicitly defined it is a 24-hour time, the am/pm isn't used.
You need to use "%I:%M:%S" for a 12-hour time.