My form views are almost at max

Is there any way to solve this problem other than upgrading?

The form views is part of the account limitations. If you wish to increase your form view limit, then you will need to upgrade to a higher subscription plan. 

If you do not wish to upgrade, then you can wait for the monthly limits to reset which happens every 1st day of the month. In this case, your form view count should reset on September 1, 2016. To learn more about form view limits, please check this guide: https://www.jotform.com/help/355-Form-View-Limits-What-is-it-all-about 

I hope that helps.