InfoPath Forms in Microsoft SharePoint Online gives you the ability to deploy your organization's forms and enable users to fill out these forms by using a Web browser. There are many ways you can configure InfoPath Forms Services depending on the needs of your organization
This article explains the Timeouts and thresholds when utilizing InfoPath with SharePoint Online in Office 365
Data Connection Timeouts:
Default data connection timeout: 10,000 milliseconds
Maximum data connection timeout: 20,000 milliseconds
Thresholds – The form operations that exceed below thresholds terminate the user session, lose all form data that was entered during the session, and generate an error message.
The Number of postbacks per session, the default value is 75.
The Number of actions per postback, the default value is 200.
The Active sessions should be terminated after, the default value is 1,440 minutes.
The Maximum size of user session data, the default value is 4,096 kilobytes.
These Timeouts and Thresholds cannot be increased in SharePoint Online.
In a hosted service like SharePoint online, the threshold configurations for different features becomes much more important for administrators and solution developers to understand. In the On-premise world, threshold issues could have been fixed with configuration changes to increased resource availability, but since these are shared environments hosted by Microsoft, the stability of the service across all customers consuming those resources must be balanced against the needs of a single service to deliver high performance and prevent DDOS attacks. One such place where this balancing can be seen is in InfoPath Forms Services
So, if you are hitting any Timeouts and thresholds described above, you need to redesign respective forms.
Below article explains configuring InfoPath with SharePoint 2010 Server