For Amazon plugins:
This usually means that your host may be blocking connections to the Amazon server. Please contact them and ask them to lift any such blocks.
If this issue results in product images not getting downloaded properly, check the option "Fetch high-resolution Amazon product image" on the "Options" page.
Those images are located on a different server.
For other plugins:
Similarly, your host may be blocking outgoing connections to sites like Clickbank.
Please contact them and ask them to lift any such blocks.