Flask web server won't respond

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I am running a Flask web app on an Ubuntu machine in an Amazon EC2 instance and I have been noticing that when I try to access the site, it just hangs and doesn't load the index.html file. The app in question has a web form and submits a URL to the server for processing (only validates if URL is between 10 and 30 characters).

This problem occurs after the server has been running for some time, but there is no consistency. It could be a few hours, to days.

I have some log entries which indicate some suspicious activity but I am not really sure how to mitigate it. I believe someone is sending garbage requests which is overloading Flask. Log entries are below, IP addresses have been masked.

Log #1

    xxx.xxx.xxx.xxx - - [31/Oct/2015 02:27:03] "CONNECT mail.mktrn.net:25 HTTP/1.1" 404 -
    xxx.xxx.xxx.xxx - - [31/Oct/2015 03:33:53] "GET /manager/html HTTP/1.1" 404 -
    xxx.xxx.xxx.xxx - - [31/Oct/2015 03:38:29] code 400, message Bad request syntax ('\x00')
    xxx.xxx.xxx.xxx - - [31/Oct/2015 03:38:29] " " 400 -
    xxx.xxx.xxx.xxx - - [31/Oct/2015 03:38:32] "GET http://httpheader.net/ HTTP/1.1" 200 -
    xxx.xxx.xxx.xxx - - [31/Oct/2015 03:38:52] code 400, message Bad request syntax ('\x04\x01\x00P\xc0c\xf660\x00')
    xxx.xxx.xxx.xxx - - [31/Oct/2015 03:38:52] " PÀcö60 " 400 -
    xxx.xxx.xxx.xxx - - [31/Oct/2015 03:39:12] code 400, message Bad request syntax ('\x05\x01\x00')
    xxx.xxx.xxx.xxx - - [31/Oct/2015 03:39:12] " " 400 -
    xxx.xxx.xxx.xxx - - [31/Oct/2015 05:10:44] "GET /manager/html HTTP/1.1" 404 -
    xxx.xxx.xxx.xxx - - [31/Oct/2015 06:02:10] "OPTIONS / HTTP/1.1" 200 -
    xxx.xxx.xxx.xxx - - [31/Oct/2015 09:39:47] "GET /manager/html HTTP/1.1" 404 -
    xxx.xxx.xxx.xxx - - [31/Oct/2015 11:24:04] "GET /manager/html HTTP/1.1" 404 -
    xxx.xxx.xxx.xxx - - [31/Oct/2015 12:24:48] "GET http://www.google.com/reader/about/ HTTP/1.1" 404 -
[/code]
Log #2
[code]
    xxx.xxx.xxx.xxx - - [28/Oct/2015 05:08:54] "POST http://check.best-proxies.ru/azenv.php?auth=144600890911134&a=PC&i=873992700&p=8080 HTTP/1.1" 404 -
    xxx.xxx.xxx.xxx - - [28/Oct/2015 05:08:54] "CONNECT check.best-proxies.ru:80 HTTP/1.1" 404 -
    xxx.xxx.xxx.xxx - - [28/Oct/2015 05:09:04] code 400, message Bad request syntax ('\x04\x01\x00P\x05\xb2VL0\x00')
    xxx.xxx.xxx.xxx - - [28/Oct/2015 05:09:04] " P²VL0 " 400 -
    Traceback (most recent call last):
      File "/home/ubuntu/anaconda/lib/python2.7/SocketServer.py", line 295, in _handle_request_noblock
        self.process_request(request, client_address)
      File "/home/ubuntu/anaconda/lib/python2.7/SocketServer.py", line 321, in process_request
        self.finish_request(request, client_address)
      File "/home/ubuntu/anaconda/lib/python2.7/SocketServer.py", line 334, in finish_request
        self.RequestHandlerClass(request, client_address, self)
      File "/home/ubuntu/anaconda/lib/python2.7/SocketServer.py", line 657, in __init__
        self.finish()
      File "/home/ubuntu/anaconda/lib/python2.7/SocketServer.py", line 716, in finish
        self.wfile.close()
      File "/home/ubuntu/anaconda/lib/python2.7/socket.py", line 283, in close
        self.flush()
      File "/home/ubuntu/anaconda/lib/python2.7/socket.py", line 307, in flush
        self._sock.sendall(view[write_offset:write_offset+buffer_size])
    error: [Errno 32] Broken pipe
    xxx.xxx.xxx.xxx - - [28/Oct/2015 05:09:04] code 400, message Bad request syntax ('\x05\x01\x00')
    xxx.xxx.xxx.xxx - - [28/Oct/2015 05:09:04] " " 400 -
    Traceback (most recent call last):
      File "/home/ubuntu/anaconda/lib/python2.7/SocketServer.py", line 295, in _handle_request_noblock
        self.process_request(request, client_address)
      File "/home/ubuntu/anaconda/lib/python2.7/SocketServer.py", line 321, in process_request
        self.finish_request(request, client_address)
      File "/home/ubuntu/anaconda/lib/python2.7/SocketServer.py", line 334, in finish_request
        self.RequestHandlerClass(request, client_address, self)
      File "/home/ubuntu/anaconda/lib/python2.7/SocketServer.py", line 657, in __init__
        self.finish()
      File "/home/ubuntu/anaconda/lib/python2.7/SocketServer.py", line 716, in finish
        self.wfile.close()
      File "/home/ubuntu/anaconda/lib/python2.7/socket.py", line 283, in close
        self.flush()
      File "/home/ubuntu/anaconda/lib/python2.7/socket.py", line 307, in flush
        self._sock.sendall(view[write_offset:write_offset+buffer_size])
    error: [Errno 32] Broken pipe
[/code]

A temporary solution I have been using is to kill the Python process and reload the webserver but that is only temporary. (nohup python run.py &)