The other genuine reason, and usually the most clear-cut.
THE SITUATION
A payment gateway, bank, API provider, partner system or corporate firewall requires connections from a specific, fixed IP address, and asks you to supply it.
On a shared IP this is problematic: the address is shared with other accounts, and giving it to a third party whitelists everyone on it, which some providers will not accept.
WHAT A DEDICATED IP PROVIDES
A fixed address used only by your account, which you can supply for whitelisting with confidence about what is behind it.
WHAT TO CHECK FIRST
Ask the third party whether they need the address your server connects out from, or the address your site is reached at. These can differ, and supplying the wrong one produces a whitelist entry that does nothing.
Ask whether they accept a shared address. Many do.
AN IMPORTANT CAVEAT
If your account is migrated to another server, the dedicated IP changes. Any third-party whitelist entry must be updated at the same time, or the integration breaks. Keep a note of everywhere the address has been supplied.
