Probably using a chat system like Livezilla can help you, as it starts a chat when support is available and creates a ticket when support is offline. Therefore, you will not miss a single customer request.
If your small hosting company has more than 3 customer support employees, you can already provide 24/7 support. Having 4 employees means possibility of day offs, having 5 means ability to have sick leaves and vacations. If you have 5+ - you are no longer small.
Outsourcing support can decimate your income, because clients do not come every hour, but you should pay for every hour outsourced employee spent providing support. Helix247 also gave great pieces of advise here.
- your content is online, always :)
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