msbuild: MSB0001: Internal MSBuild Error: Node does not have a provider.

We got a report of an intermittent msbuild failure (~once every 2 weeks) with the following message:

UNHANDLED EXCEPTIONS FROM PROCESS 4544: 
===================== 

Microsoft.Build.Shared.InternalErrorException: MSB0001: Internal MSBuild Error: Node 2 does not have a provider. 
at Microsoft.Build.CommandLine.MSBuildApp.BuildProject(String projectFile, String[] targets, String toolsVersion, Dictionary`2 globalProperties, ILogger[] loggers, LoggerVerbosity verbosity, DistributedLoggerRecord[] distributedLoggerRecords, Boolean needToValidateProject, String schemaFile, Int32 cpuCount, Boolean enableNodeReuse, TextWriter preprocessWriter, Boolean debugger, Boolean detailedSummary) 
at Microsoft.Build.CommandLine.MSBuildApp.Execute(String commandLine) 
at Microsoft.Build.CommandLine.MSBuildApp.Main() 
=================== 

Context details: 6 C# projects, built on VS2015. The solution is a VS2010 solution with target .net 4.0.

Cmdline (with replaced project names): Executing the command cmd.exe /C " “C:\Program Files (x86)\MSBuild\14.0\Bin\msbuild.exe” /t:Clean,Build /P:Configuration=Release;Platform=x86 /maxcpucount ProjectFolder\Project.sln " && exit %%ERRORLEVEL%% from H:\Jenkins\workspace\Dev_Build [Dev_Build] $ cmd.exe /C " “C:\Program Files (x86)\MSBuild\14.0\Bin\msbuild.exe” /t:Clean,Build /P:Configuration=Release;Platform=x86 /maxcpucount ProjectFolder\Project.sln " && exit %%ERRORLEVEL%%