The registrar APIs are only for importing your domains and their details, they do not keep the expiry dates updated automatically.
What exactly happens when you try to import from your NameSilo account? Does it give you an error, does it import your domains but not their details, etc.
A couple things to check...
1) Edit your NameSilo registrar asset (the registrar, not the registrar account), and ensure that the "API Support" has NameSilo chosen
2) Edit your NameSilo account asset and ensure that your NameSilo API key is entered correctly