I see that you are still running version 7.5.5, released February 10th, 2010
It looks as though your issue could be caused by database charset collation issue. Have you recently changed your database structure. It could also relate to if your web host has updated their MySQL or PHP versions lately.
I say this especially because I am able to use that character in my post to your site, and preview it, before posting it to your database. (see attached screenshot)
Have you also recently changed from "utf-8" to "iso-8859-1" ?
In addition, I noticed that your page header has several errors in it, which could also cause page display issues.
UNRELATED: Please use a NSFW tag on your link, since it does contain photos of women in string bikinis.
Changes to the MySQL Server, PHP, or Apache are done either via techs at your webhost, automated tools on your server, or by a technician you hire on your server (for VPS and Dedicated servers); these are various upgrades to the base system that are generally seen as requirements for features and security (IE, if there are/were changes, they probably weren't done by you unless you're comfortable with managing the backend of a server).
Like Isaac said, it sounds like your database is expecting the data to be in one format, but the forums are presenting it in iso-8859-1; more recent versions of UBB.threads (namely v7.6.0) fixes quite a lot of problems over past releases.
If you look at the UBBWiki posting "UBB.Threads Changelog Index", you're running v7.5.5 (February 10th, 2010) whereas the latest is v7.6.0 (February 15th, 2017). There have been a vast number of improvements over the 7 year span since your version was released (if you click on a release it'll show you the developer notes).
Can understand updates took place between my version and the latest version. However it makes no sense it just started yesterday with none of these issues prior to that. No changes to the board have been made.
Contact your webhost, inquire as to the last updates they've made to the server you're hosting on. They likely upgraded PHP and a number of items; keeping system software up to date is common, breaking things is also common (an example would be UBB.threads is completely unable to be run on PHP7, which is becoming a common build of PHP).
There is very little we can do to aid in system issues, and all we can really do with a lot of software issues is suggest running a current build as bugs are fixed in incremental builds (plus, this is a user to user support forum and we only support current builds; Isaac and I are contractors, we do not own or otherwise work for UBB.threads).
Contacted hosting service. They have made no changes. Could there be some kind of errors with the forum itself. Odd that it would start a few days ago. Back to square one. I shouldn't have to upgrade to have something this basic to work properly.
There have been significant improvements to the coding since v7.5.5 was released on February 10th, 2010; several of which have to do with web standards changing over the years, new functionality, support for newer versions of PHP (generally compatability), etc.
It's basic evolution of web technology, such as how UBB.threads will currently not run under PHP7, PHP5.4 being required to run v7.5.7+, PHP 5.3 required to run UBB.threads v7.5.4+, etc.
As you said, nothing has changed within your UBB.threads forum, which leaves server side changes.
the extended char set storage is controlled within your mysql database. it’s also passed there through php. and stored in the defined charset collation format. all of those things are controlled on the server side and not any setting which is within the UBB.threads software except for the method at which the chars are checked before being passed from the webform to the database storage. That is handled by a php module and the php function which parses it (code within the ubbthreads software). this has been updated over the years. but this would be the only piece of your current forum software which definitely has not been touched/changed (according to you) at all. so what has probably changed is a server side php module update or mysql charset storage adjustment.
maybe the issue may even be the browser converting the char from the outdated iso-8859-1 set of tour forums to the utf-8 set. though I dont believe that is related at all, since it still displays in the preview.
tldr; something on your server was updated. maybe it might be time to use human searchable fractions rather than extended chars, which are primarily only available to word processors. mobile device and traditional 101/104 keyboard layouts do not have dedicated fraction keys. In addition, fractions are rarely, if at all, indexed by the major search engines, and even less likely to be used when a human is searching for specific results.
these are the only answers I can come up with. I wish I could be of more help, but that’s all I have for you, which is based on my experience and the information already shared in the above posts.
(excuse my caps/typing. posted with my smartphone)