This is a problem with IE.
SSRS uses the <Title> tag in the generated html for tooltips, which is subject to a setting on your machine. It's not a setting that you can change either in the report or on the report server. From previous research there is supposed to be a registry entry that controls the bubble tool tip delay but the only ones I've been able to find are for the explorer tray and the start menu, not for IE.
I've tested tooltops in both Chrome and Firefox, and the tooltips in there stay on screen for ages as long as you hover over the cell. They also re-appear if you move the mouse away and back, unlike IE which only shows them once. It's frustrating that IE doesn't do that given that if you are using SSRS in your organisation then chances are they are using IE as well.
The workaround as suggested by MSFT
or by using a reportviewer control in a custom web application to display the report.
A really simple workaround is to use an alert
(window pops up that requires you to press OK to close it).
Personally I think Chrome is the better workaround, many reports don't render properly in Firefox so that's not a solution. The real answer would be for MSFT to fix the <Title> tag behaviour of IE, but it's been a problem for years and there is probably some reason they don't do it. They could either provide an easy setting to modify, or ideally make it indefinite. The worst part is that it displays for 5 seconds and then you can't get it back without refreshing the report!