Say I make a few backup copies of my Bitcoin Core wallet and save those copies a few different places. I then continue using the original wallet for a few moths adding new funds to it. Will the backup copies I made earlier automatically have those new funds on them if I lose the original wallet or does the original wallet need backed up again every time new funds are added? Thanks for any responses.
That depends.
Are you using the latest version and using the default HD (Hierarchical Deterministic) functionality, or are you using an older non-HD version of the wallet?
Have you changed your password since you created the backup?
How many transactions have you sent, and how many receiving addresses have you requested from the wallet?
If you are using the HD wallet, and you have not changed your password, then the backup copies you made earlier will automatically have those new funds on them. If you have changed the password, then they might not.
If you are using the older non-HD wallet in default configuration, and the total number of transactions sent PLUS the total number of receiving addresses requested since the backup is more than 100, then the backup copies you made earlier will probably automatically have those new funds on them. If the sum is more than 100, then they might not.