The email server isn't responding so instances have been suspended at "Email Service Task" task. How do i go around this to ensure the process continues without sending emails please?
If you remove the email task from the affected business processes then they should automatically continue. However, this is just a quick fix. As far as I know there now way to detect and respond to errors in a Forms business process. In the latest version of Forms there is a new setting you can enable that will at least email you when thing enter a suspended state, which is something I know many of us have been asking for a long time. So you can at least be made aware as soon as the issue arises and quickly respond.
In Forms 10.4.2, we added the skip functionality for suspended email service task. https://support.laserfiche.com/kb/1014083/list-of-changes-for-laserfiche-forms-10-4-2. You can upgrade to the latest version of Forms to use this feature.