This bug is fixed upstream (or at least I can't reproduce it):

2016-05-03 14:49:43,468 ERROR: Virt backend 'env/cmdline' fails with exception:
ConnectionError: ('Connection aborted.', BadStatusLine("''",))
2016-05-03 14:49:43,469 INFO: Waiting 60 seconds before retrying backend 'env/cmdline'
2016-05-03 14:50:43,896 INFO: Report for config "env/cmdline" hasn't changed, not sending

Fixed in virt-who-0.17-1.el7.

Verified it on virt-who-0.17-2.el7.noarch since virt-who won't generate too many redundant info and throw error info when can't connect proxy. After proxy can be connect, virt-who still work normally. Therefore, verify it.

Verified version:
subscription-manager-1.17.6-1.el7.x86_64
python-rhsm-1.17.2-1.el7.x86_64
python-rhsm-1.17.2-1.el7.x86_64

Verified process:
1. Register system to Satellite6.2
2. Configure virt-who run at esx mode and make virt-who connect vcenter through proxy. then restart virt-who service.
3. Restart squid on proxy
[root@samdns ~]# service squid restart
4. Before squid is restarted, check the virt-who's log 
2016-06-02 03:09:56,001 [virtwho.test-esx1 ERROR] Esx-1(11146):MainThread @virt.py:run:377 - Virt backend 'test-esx1' fails with exception:
Traceback (most recent call last):
  File "/usr/lib/python2.7/site-packages/virtwho/virt/virt.py", line 372, in run
    self._run()
  File "/usr/lib/python2.7/site-packages/virtwho/virt/esx/esx.py", line 174, in _run
    options=options)
  File "/usr/lib/python2.7/site-packages/suds/client.py", line 542, in __call__
    return client.invoke(args, kwargs)
  File "/usr/lib/python2.7/site-packages/suds/client.py", line 602, in invoke
    result = self.send(soapenv)
  File "/usr/lib/python2.7/site-packages/suds/client.py", line 641, in send
    reply = transport.send(request)
  File "/usr/lib/python2.7/site-packages/virtwho/virt/esx/esx.py", line 95, in send
    verify=False
  File "/usr/lib/python2.7/site-packages/requests/sessions.py", line 507, in post
    return self.request('POST', url, data=data, json=json, **kwargs)
  File "/usr/lib/python2.7/site-packages/requests/sessions.py", line 464, in request
    resp = self.send(prep, **send_kwargs)
  File "/usr/lib/python2.7/site-packages/requests/sessions.py", line 576, in send
    r = adapter.send(request, **kwargs)
  File "/usr/lib/python2.7/site-packages/requests/adapters.py", line 415, in send
    raise ConnectionError(err, request=request)
ConnectionError: ('Connection aborted.', BadStatusLine("''",))
2016-06-02 03:09:56,002 [virtwho.test-esx1 INFO] Esx-1(11146):MainThread @virt.py:run:390 - Waiting 60 seconds before retrying backend 'test-esx1'
2016-06-02 03:10:56,065 [virtwho.test-esx1 DEBUG] Esx-1(11146):MainThread @esx.py:_prepare:127 - Log into ESX
2016-06-02 03:10:56,291 [virtwho.test-esx1 DEBUG] Esx-1(11146):MainThread @esx.py:_prepare:130 - Creating ESX event filter
2016-06-02 03:10:56,412 [virtwho.test-esx1 DEBUG] Esx-1(11146):MainThread @virt.py:enqueue:357 - Report for config "test-esx1" gathered, putting to queue for sending
2016-06-02 03:10:56,414 [virtwho.main INFO] MainProcess(11139):MainThread @executor.py:run:250 - Report for config "test-esx1" hasn't changed, not sending

Result:
virt-who won't generate too many redundant info and throw error info when can't connect proxy. After proxy restart successfully, virt-who still work normally.

Since the problem described in this bug report should be
resolved in a recent advisory, it has been closed with a
resolution of ERRATA.

For information on the advisory, and where to find the updated
files, follow the link below.

If the solution does not work for you, open a new bug report.

https://rhn.redhat.com/errata/RHBA-2016-2387.html