Iphone 5 Wi-Fi keeps turning off and on?

I have had an iPhone 5 for about 6 months with nothing really happening or wrong with it, however, suddenly yesterday my phone had disconnected from my Wi-Fi. I thought it was weird because my router is literally right next to me. So I reconnected my Wi-Fi on my iPhone and it connected, but it disconnected a few seconds later. It kept disconnecting for a few seconds then connecting for a few seconds. I had reset my router and modem but it doesn't seem to change anything. My family's iPhones do not have a problem connecting to the Wi-Fi so I do not have a problem with my router. I have even reset my network settings but that didn't do anything either. My iPhone is jailbroken but had no problems with it until yesterday night (or this morning) about 4 am. Please help, I really don't know what to do and I really don't want to restore my iPhone.

Added (1). To be clear, there's nothing wrong with my internet. It works fine and the iPhones connect to the Wi-Fi normally.

Call your internet service provider and ask for a refresh on your internet.
Give them a minute, and your internet will be as fast as when you first got it.
A refresh is just getting rid of old server data, nothing will be lost.
(just make sure they don't delete your internet username and password)

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