How to prevent an Azure website from going to sleep?
Azure Web Apps have an 'Always on' option (with basic/standard tiers) which keep your app (and associated web jobs) loaded.
Look under Settings, and you'll see 'Application settings':
Then look for the 'Always on' setting (which will be disabled for Free tier):
I know this post is a little old, but the issue is still relevant.
I use a free service called Uptime Robot - https://uptimerobot.com/
Even on the free tier, you can create up to 50 monitors to call your web site, at least every 5 minutes, which is certainly regularly enough to keep your site alive.
As well as keeping the site alive (without any knock-on consequences of using 'Always On') it also serves as a monitor for your site, letting you know if it's down.
You can create monitors that alert you if specific words are in or not in the response, so it's quite easy to check the content is correct. You could even create a 'test' page that just returns 'OK' after checking various functionality on your site.