Update, Refresh, or Stall

To buy yourself some time, let a client know that you've seen their request and will be getting back to them as soon as possible:

Hi [FIRSTNAME],
Just wanted to let you know I've seen your support request, and will be taking a look as soon as possible. We'll get you taken care of shortly. Thanks! Have a great day.

To buy yourself some time after you've engaged with the client, but still haven't resolved the issue, let them know you're working on it:

Hi [FIRSTNAME],
Just wanted to let you know that I'm working on your case here, and will be getting back to you as soon as I have a resolution! Thanks for your patience.