Veeam Agent for Microsoft Windows backup job fails with "Veeam.Backup.AgentProvider.AgentClosedException" on Windows 7 and Windows Server 2008 R2

A Veeam Agent for Microsoft Windows v6 Backup Job for a machine running Windows 7 or Server 2008 R2 fails with the error:

Exception of type 'Veeam.Backup.AgentProvider.AgentClosedException' was thrown.

When this occurs, the following error can be found in the Windows Logs > Application event log:

Log Name: Application
Source: Application Error
..
Event ID: 1000
Task Category: Application Crashing Events
Level: Error
Keywords: Classic
Description:
Faulting application name: VeeamAgent.exe, version: 6.0.0.960, time stamp: 0x63dd15c4
Faulting module name: KERNELBASE.dll, version: 6.1.7601.24384, time stamp: 0x5c6e248c
Exception code: 0xc0000005
...
Faulting application path: C:\Program Files\Veeam\Endpoint Backup\x64\VeeamAgent.exe
Faulting module path: C:\Windows\system32\KERNELBASE.dll
...