download the flashplayer installer from a reputable site. e.g. filehippo.com
select the appropriate program depending on the default browser you use - internet explore or non-internet explorer.
in filehippo's case, you will have to initially select the proper beta file. at the far right column, there will be the option to select and download the latest non-beta file. 10.0.42.34.
i would disconnect and shut down the browser and all windows associated with the browser. install flashplayer.
reconnect. visit adobe.com/shockwave/welcome. that site will confirm the installation's success, or not.
of course, if firefox and noscript addon, then johnem's advice applies.
if it's a particular favorite site that informs you of the need to update flashplayer, then it may be the fault of that website. this past summer, i had that problem with a site. everything else checked out. eventually, the site "updated" and everything was well.
If you are using Internet Explorer 7 or 8 then check 'manage add-ons' through tools. Under 'show' select 'all add-ons'. First one should be Shockwave Flash Object and enabled.
Second one should be Shockwave ActiveX Control and also enabled. Next time you reboot the laptop check that these two add-ons are enabled. If they are disabled then possibly a security program is being overzealous.
Sounds possibly like a security program might be disabling Flash on boot. Seem to remember a thread with WinPatrol doing something similar to this. Try reinstalling Flash again and rebooting to safe mode with internet connection. See if Flash is running ok.