PsExec and invalid handles

Question 1

You need to debug the situation.

You have a script, then something (what is Jenkins?) launch it on a remote PC, sometime it works, sometime it fail.

Is it deterministic?
When it fail does it always fail?
How does it fail?

You need to acquire better knowledge of how/when the script fail.

Here is what I would do to gather better understanding of these fails.

Can you run the script multiple time?
From the comments it seem that you run the script every hours, can you run it 3/4/5 time in a row, for each hours?
This will help you to determine how it fail: if you run it 5 time, does it works every time? it it fail, does it fail 5 times in a row?

Can you try to use different script?
You can create some more similar, but simpler, scripts.
So you can try your script with the RMDIR, then another script with a simple DIR command (just to se if the script launching/connection mechanism works) then another script with a simple ECHO command (so it doesent need to access any files/folder)

Run debug scripts on the local PC
Then, you can simultaneously run other scripts that run on the LOCAL PC (not the remote one where you need to execute the RMDIR) that try to access the remote PC, with a PING, or by copying a file from/to a network share...

Sniff the network
You can even set up a Wireshark instance that log all the packet sent between the 2 PC, this can be helpful to analyse/exclude networking issue.

You clearly need to track/log everything.

With this kind of information maybe you/we can have a better understanding of where the issue is.

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UPDATE 1 - Record some log

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Maybe you can try to use the following modified scripts to have some log files. These script will create 2 log files, one on the remote PC (containing the message of the remotely executed command) and one on the local PC (containing any message from PsExec)

(you'll need to tweak the path where the log file are saved)

psexec %HOSTNAME% -I -u %USERNAME% -p %PASSWORD% CMD /C "RMDIR /S /Q e:\SomeDir >>c:\RemoteComputer.log 2>&1" >>c:\LocalComputer.log 2>&1

or the following one without the /I
Are you sure you need the /I parameters for CMD? On my Pc it doesn't works if I use the /I parameters...

psexec %HOSTNAME% -u %USERNAME% -p %PASSWORD% CMD /C "RMDIR /S /Q e:\SomeDir >>c:\RemoteComputer.log 2>&1" >>c:\LocalComputer.log 2>&1

After some testing on my PCs, I've seen that PsExec install a service on the remote PC to run the command remotely. (It's called PsExecSvc.exe, installed in c:\windows\ on the WinXP PC I'm using for this test)
The remote installation/uninstallation of this temporary service for the command execution can surely be one of the possible "failure point" that generate the error.
If this is the case, then you should be able to track this down by looking at the LocalComputer.log, that will contain the message/error from PsExec.

As stated in my previous advice, I would also try to schedule simpler script like

psexec %HOSTNAME% -u %USERNAME% -p %PASSWORD% CMD /C "dir c:\ >>c:\RemoteComputerDir.log 2>&1" >>c:\LocalComputerDir.log 2>&1

and

psexec %HOSTNAME% -u %USERNAME% -p %PASSWORD% CMD /C "echo SuperEchoTest >>c:\RemoteComputerEcho.log 2>&1" >>c:\LocalComputerEcho.log 2>&1

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UPDATE 2 - Try to use WMI

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You can try to run the remote command by using WMI

wmic /node:%HOSTNAME% /user:%USERNAME% /password:%PASSWORD% process call create "CMD /C RMDIR /S /Q e:\SomeDir"

When you use WMI you need to be sure that windows firewall is not blocking your command. (when I tried to run a remote command with WMIC the windows firewall notification popped up on my Win 7 PC)
(I've the instruction to use WMIC here)

Question 2

Yes, there is a more reliable technology for executing commands on a remote machine and is called powershell. For example, you can run :

test-connection -computername server01, server02, server12

pings from local computer to several remote computers.

Another very useful command is:

invoke-command -filepath c:\scripts\test.ps1 -computerName Server01

runs the Test.ps1 script on the Server01 computer.

A tutorial gives several examples on how to Run PowerShell Commands on Remote Computers.

Question 3

A different technology can be found mimicking the Linux world, and using ssh. It's very common with clusters and I have personally used it with Windows Server 2008 R2, so I don't expect any difference on windows 7.

This task is commonly performed with ssh and password-less public key authentication. With it, the only needed information is the IP of the remote server and the public key of the client, stored on the server: only the client with the corresponding private key can connect to it (the keys must be created with ssh-keygen, on the client. The public key is copied to the server)

The server must have the TCP port 22 accessible from outside, in case there are firewalls, NATs,...

In my case I used the ssh server included in Windows SUA, but I suggest you forget them (they are deprecated, and quite cumbersome actually) and give a try to the OpenSSH cygwin server, sshd - even if not officially Microsoft, there is a large community supporting it at least - and occasionally I have used it reliably.

The client ssh command is included in SUA, in cygwin, or you can use putty if you want a lightweight solution on the client (not that cygwin is heavy - just the burden of having a sort of linux emulation that's not needed)

Giving a search for example I have found this post, explaining well the needed steps.