I know that a lot of you have more knowledge of Windows-platforms than me,
That's dependant on specific information you give and specific Windows version. Some are fixed in Service packs releases(e.g Q317288).
Check Microsoft’s knowledge base website for any issue which deals with DHCP and shared internet access.
However, instead of connecting and staying online, it is periodically being connected and disconnected. The periods are seemingly irregular.
Without further information, one could only guess at the problem.