I've upgraded to 3.1.0 beta 38 and sent an encrypted, non-signed e-mail to myself.
The received e-mail was shown unencrypted in inbox. See log-file below.

Behavior is the same as 3.0.3 /3.1.0beta32.
It reads encrypted e-mails if Titus plugin is disables (GpgOL as the only plugin).
Strange: Both beta32 and beta38 show the recipients box after pressing the send button, but
the messages are sent unencrypted. After downgrading to 3.0.3 messages are sent encryted,
again.

Version 2.0.7-beta6
Test 1 (without S/MIME support):
encrypted e-mail shown as plain text (-----BEGIN PGP MESSAGE----- ...), can be decrypted via clipboard and GPA.
Sent message shows same plain text as received one.
No encryption icon in Outlook Inbox.

This is the log output for sending a GPG message to myself:

All e-mails I tried to open with 2.0.6-beta7 gpgol.dll were readable and showed the correct content in my environment, now. Great!

A signed but not encrypted message appears in the same way (visible in Sent, empty in Inbox)

Looking at the messages from above using another PC, same Windows 7 and Outlook 2010 but Gpg4Win 2.3.3 :

• received message in Inbox is decrypted shown correctly inline both in preview and opening it
• original message in Sent is not decrypted, but shown as encrypted with gpgolXXX.dat attachment

Hence, it shows the opposite behavior to the 3.0.2 handling.

One problem seems to be that the content of Inbox message differs from this one in the Sent folder (10 vs. 20 KB).
The content of the Inbox is shown as empty, even using the "show source" option. Saving the message as plain text shows a PGP part inside, but this is ignored by Outlook.
I tried this advice:
How to view the message source in Outlook
But the result is the same, after maked as read, the message becomes unreadable.

• fresh install of Gpg4Win 3.0.2
• reboot
• openening Outlook 2010 with only one plugin (GpgOL)
• sending an encrypted email to myself
• trying to open that email (no content)

@aheinecke Because it was mentioned in another comment, I've tried to restart Outlook with the GpgOl plugin enabled, only. Same result. But the fact that I could see the message just after arrival, but not in a second approach may point in a direction that incoming messages are processed by an server-based filter changing potentially vulnerable email content (as embedded links).
I could try to log the complete process of sending an email to myself, decrypting once and failing in a second trail. This would actually increase the size of the log file.

Just installed Gpg4Win 3.0.2.
Had a very similar effect with Windows 7 / Outlook 2010:

• Sending an encrypted e-mail to myself.
• E-mail will be decypted once after receiving.
• After that, e-mail is shown as "unsecure" and with empty message body (both in preview and own window).
• E-mail in "Sent" folder still decryptable with right content.

I've added gpgol.log for opening Outlook again after receiving the e-mail (with empy body, now).

Update: It was my mistake (typical beginners failure): I had to create gpg-agent.conf instead of usig gpg.conf.
Adding disable-check-own-socket resulted in the right behavior, till now:
After some time-out, GpgOL asks for password again and decrypts the content as expected.

Could confirm a similar behavior with Windows 7 and Outlook 2010 using GPG4Win 3.0.1.
Time frame for loosing the decryption ability is about one hour or more.
Setting disable-check-own-socket in gpg.conf (didn't find gpg-agent.conf) resulted in "no data" error on all
encrypted e-mails.

@aheinecke From a first glimpse, I think we got it. Great work!
I replaced both versions of gpgol.dll as adviced (surprisingly /bin was locked, I expected /bin_64 ).
Thereafter Outlook decrypted all "old" message instantly and without any problems.
Thanks for the effort you spent and the fast reaction time!

Two versions of the same message as shown in the comment of 24th Nov.

It could depend on the formatting in Outlook (changing hyphens etc.), e.g.
-----BEGIN PGP MESSAGE----- looks sometimes different in Messages.

I've sent an email from Outlook using version 2.3.3, to myself. What I see in Outlook with version 3.0.1 is:

-----BEGIN PGP MESSAGE-----
Version: GnuPG v2
hQEMA6jFcgdYY5bVAQgAhWTqExXJVk3aPC5rKYFUeb0NSR+TtChjBzxBrFzQ5qDr
trJiT6o7XoFYDKwdJFXMv81Zcetsu/dOq3dPoCpaQDAtna8xshJDogsx7bOV5bvO
9kLzegZqUk4RzAJLCOTkIISh/Qi6o6kXL4+Iwm17FKfVb0MSAjmrOV50SevrKpD+
PxEYr7BJHRwA9HcYMCb1tvao74AFShZV2olEuwuGvF2nuuqTl6MngKI0Qhteds3F
B6MPOckhHvOCLr3u1z7ld+svggaVFhPyTbXuGxTXAHyieeUr0yf+p4UufdTj3XTn
L/ZeK7l0TKJykbWZmFfZFDClyEDvQx1Vq7ggLuIbh9I/Ab/LkshjC+QGFmfpVaH/
D03ZQv+RStnlI3ZVWvWsAxsaWp/hEsP4RHkmVQXhI4YeRBw1e6TeXzvTvMidjnBC
=oLiX
-----END PGP MESSAGE-----

In the GpgOL ribbon the button shows a question mark and an "unsafe" label.

Just installed Version 3.0.1. From a first glimpse, it seems to work more stable in Outlook context.
But decrypting older plain text messages still fails.
Using GPA (copying PGP ASCII text into dashboard) decrypts contents without error.
-----BEGIN PGP MESSAGE-----
Version: GnuPG v2
...
-----END PGP MESSAGE-----