I'm attempting to send emails from or access a third party service and am getting errors saying the IP address the request is coming from is being blocked.
Unfortunately, this happens from time to time on our platform. We take a wide variety of measures to help ensure that it happens as little as possible, but due to the variety and volume of applications running it's not uncommon for some IPs on our platform to be blocked for periods of time.
If the upstream service requires a stable IP address for them to explicitly allow, many of the Network Services add-ons offer a fixed, or small pool of fixed outbound IP addresses for your application. This is a great solution to help ensure you're never bothered by other applications also using the same IP address since you can guarantee that your dynos will make requests from a "clean" IP address that you control.
Performance dynos typically are also less affected due to their single-tenant nature. They're more costly, but if that's an option for you it's worth considering depending on how critical this is for your application.
Finally, Heroku Enterprise customers can make use of Private Spaces to ensure that predictable static IP addresses.