No, there is no limit to the number of cap tables one can download.
However, one credit is deducted from your account for downloading one company's Captables from the platform.
Once the CapTable is downloaded, and you want to download the same CapTable in the future, you can do so from your Export History.
You can view more info about Credits here
Captables can also be requested on-demand for companies based out of the geographies covered by clicking the "Request For Cap Tables" button on the Company Details Pages of that particular company, or via any of the support channels.
No credits are deducted for such requests. However, this option is offered as per the fair usage policy of the platform and the option can be rescinded if misuse is found or a high number of requests are placed in a very short period of time.