Well I don't believe that prolonged periods with the laptop on would have any impact on connect/browsing speed.
Turning it off would restore any memory which had been used and you are starting from square one again, but I still feel any increase in speed isn't down to rebooting unless your system is so low on resources that it might effect browsing, which might be cpu/memory intensive.
What is your OS, CPU, RAM ?
What are you doing when this slow down occurs ?
Ensure that only essential programs run on boot, typically security programs, many programs when installed set themselves up to run on boot when they aren't essential. For example media players, they only need to run when you click on a media file.