From a philosophical/technical standpoint, no. In order to verify this we would need to visit your site every second of the day, which would cause significant load on your servers.
From a practical standpoint, yes. If you have continual failures at your site that are not the result of site updates or configuration changes you have made, it is unlikely the ISP is meeting your 99.99% uptime guarantee. 99.99% means less than 5 minutes of downtime per month. Our customers often take our raw logs back to their ISPs to use as ammunition to get their systems fixed, or to renegotiate their Service Level Agreements (SLAs).