The HTML formatting is stripped in the signature.
There are a few reasons this can happen in replies while the signature is displayed as intended on receipt of the original message.
There is an Outlook setting that does this by default to reduce the size of the email message. This could effect any conversation thread.
- Open Outlook (2010, 2013, or 2016 for Windows)
- Click File > Options > Mail.
- Scroll down to Message Format and uncheck the box that reads: "Reduce message size by removing format information not necessary to display the message"
If this only happens when replying in threads with certain senders or recipients their email client(s) may be sending email in Plain text format instead of HTML this could be a setting in their email client. Some clients only send in RTF or plain text, and some include settings to modify the format.