I am using windows 7 where whenever the system gets into sleep mode, a software deals with network check stops generating logs of the network.
I don't understand why the software stops working in the sleep mode.
How can I overcome this problem?
Windows 8.1 and 10 have support for connected Standby and modern standby, respectively. These modes are different from standard S3 low power mode, and allow basic connectivity for Windows store apps.
Windows 7 and previous are going to be using an s3 state, where all software is suspended in ram and most hardware devices are powered down. As such, there is no way to do what you're hoping in Windows 7. You will need to disable sleep mode, or wake the machine up to do it's tasks.
It may be possible using a modern UI app in Windows 10, but this will require compatible hardware and specialised software development for it.