Channeltivity integrates with your account through the webservices API. Channeltivity's integration with Salesforce is fairly conservative with its usage of the Salesforce API and you shouldn't run into any limits. However, if you have other applications that make extensive use the Salesforce API, you may run into the Salesforce REQUEST_LIMIT_EXCEEDED error. 

Salesforce places limits on the number of API calls that can be issued against a given Salesforce account in any given 24 hour period.  If this threshold is exceeded, Salesforce may block incoming webservice calls until the volume falls below the threshold. 

These Salesforce API thresholds are based entirely on your contract with them. If your current Salesforce account does not provide enough API calls to accommodate your needs, you may need to negotiate this threshold with your account manager.

How to check your Salesforce API Usage in Channeltivity:

Go to the Salesforce Sync Manager Page (Settings > Salesforce Integration > Sync Manager) and you'll see the Salesforce API calls made by Channeltivity in the last 24 hours:

How to check your API Usage in Salesforce:

Step 1: As an Administrator, go to the Setup link at the top of the screen:

Step 2: Click on the "Company Information" link under "Administration Setup" and "Company Profile" in the side navigation:

Step 3: Your API Request usage is on the Organization Detail page:

Note: if you don't see the API Requests number, it could be because your Salesforce instance doesn't have the API enabled. Only Salesforce Enterprise Edition includes the API by default. Salesforce Group and Professional Edition don't include the API, although you can pay to get API access with Professional Edition. 

System Administrators can also access an Administrative Report  on API Usage in the "Reports" tab to see if there are any other applications that are using your Salesforce API calls:

If you're looking for more detailed reporting on your Salesforce API usage, here's an article that explains how to Export Salesforce Event Logs for viewing.