The way the Select By Attributes dialog box is set-up means that just by clicking this box (not necessarily clicking the drop down – but clicking in the box and pasting a value) queries the service for all distinct values.
This doesn’t scale very well, and in our case, we are working with a point feature service of over 10 million features. What ends up happening is when the box is clicked, the tool spins until a 504 timeout error occurs in the backend (we figured this out by capturing a fiddler log).
We can work around the issue by toggling on the ‘SQL’ option before searching for a specific value, but we would like to request that simply clicking on this box should not complete any queries – it should wait to query until you click the drop down button.