First of all: your find processes are not escaped, so that the wildcards * are transformed.
To prevent that you can either use backslashes \ or use single-quotes '
So:
find . -type f -name '*-23May2017-10-00hrs.log' -print
should work fine.
Back to your real questions:
There are several ways to solve that. First you can use find's -mtime feature to just listen every file which last modification is x minutes ago.
Let's assume your sip server logs at /var/log/sip/
find /var/log/sip/ -type f -name '*.log' -mmin +$((24*60)) -print
will show you every file ending with .log and which last modification was 24*60 minutes (1 day) ago.
However you can also use a tool which is made for logging handling and thats logrotate.
logrotate is available on every major unix distribution and allows you to compress files at a certain age, remove them at another ago and so on. The feature list is quite long.
It's easy to install, runs as a daemon and you don't have to fiddle around with extra cronjobs.
My suggestions is to use logrotate. Check out it's simplicity at: https://linux.die.net/man/8/logrotate
logrotatefor that job.