Availability monitoring service with low checking interval

Nagios check_http plugin can do this assuming you tweak the timeouts, however you are likely to get quite a few false alarms. The plugin checks do get queued and occasionally the system delays the outgoing network calls. Having such a low timeout can trigger a temporary fault.

Best suggestion, leave the check interval at every minute but set the timeout to 10 seconds (or lower). Then leave the re-try checks to 2 so it will alert on 2 failed checks.

The other alternative if you are only doing a few sites is to script something up that checks the site and fires off an email on X number of bad checks.

I know Zabbix provides the functionality that you are looking for. You can check HTTP connectivity and get alerted on latency too. Same is achievable in Nagios too, matter of writing the plugin if not already available. For third party providers I know Gomez provides monitoring solutions.