You didn't specify which device you have.
Do have enough free memory in your phone?
Try going to:
-> Next to personal applications and click on the symbol in the form of a list
-> Tick "show system apps" then press OK
-> Scroll through apps until you find "Software Updates"
-> Click on it then go to "Storage Memory"
-> At the bottom right click on "Empty Cache"
-> Restart your phone and try again to check for updates.
If you have a recent device, most likely you are having problems with your Wi-Fi connection.
You need to have a Wi-Fi connection in order not to have download problems