Macbook Pro 2011 Wifi stops working after a few minutes, needs PRAM reset to get working again
I would start with something simple and boot into Safe Mode and test how well your Wi-Fi works while in Safe Mode.

Follow these steps::


Fully shut down your MBP
Restart your MBP
Immediately press the Shift key and keep it down 
Let go of the Shift key when you see the login window (NOTE: If you have FileVault enabled you may need to log in twice. Also note that booting into Safe Mode can take a while!)
Take a note of what happens (i.e. can you now connect to the Wi-Fi network and stay connected?)
Exit Safe Mode by restart your MBP as normal and test again


The act of booting into Safe Mode will actually perform a number of background tasks, and this often resolves issues when you've rebooted normally.

Once you've tried the above let me know how you go.

[Update 1]

Since we've established the issue is still present during Safe Mode and that it still keep recurring after resetting NVRAM, let's next test your hardware for signs of any problems.

Run Apple Hardware Test

Your model MBP uses Apple Hardware Test. To use this, follow these steps:


Shut down your MacBook Pro 
Restart your MacBook Pro
Press and hold the D key before the gray startup screen appears.
After a while, Apple Hardware Test (AHT) will start.
When prompted, select your language and click the right arrow. 
When the AHT console appears, you can choose to run Basic tests by clicking the Test button. However, I suggest you select the "Perform extended testing" checkbox before you click the Test button.
Your test results will appear in the window in the bottom-right of the console.


Note 1: that the extended test will take some time. Take a note of the results and report back. 

Note 2: If pressing and holding the D key at Step 3 doesn't work, start again at Step 1 and, at Step 3 press and hold both the OptionD keys instead. This will try and run diagnostics from the internet instead, so you will need to allow more time for it to complete.

[Update 2]

Another option worth trying is to remove your Wi-Fi service, restart, and add your Wi-Fi service back.

To do this:


Go to Apple > System Preferences > Network
Select the Wi-Fi service on the left-hand side
Click on the cog icon at bottom-left and select Make Service Inactive
Now delete the service by clicking on the minus sign (i.e. the - button) at left of the cog
Click on the Apply button
Exit Network preferences
Restart your MBP
Go to Apple > System Preferences > Network
Click on the plus sign (i.e. the + button) at left of the cog
In the pop-up window, ensure that Wi-Fi is selected from the drop-down menu
Click on the Create button
Make sure Wi-Fi is on and connected (it should remember your previous settings, but if not just re-add your Wi-Fi network again)


Let me know how you go.