Riaaz,
Entering that regular expression in an online regex tester such as http://www.regextester.com/ results in syntax errors on the + operator so I'm not surprised its failing.  Fixing the syntax errors would result in this:
^([0-9a-zA-Z]{8})+((,[0-9a-zA-Z]{8})+)*$

What is the pattern you are hoping to match with this regular expression?  I imagine the intent was to allow an 8 character string consisting of letters or numbers, or a comma separated list of such strings.  The modified regex I provided above will allow that, but would also allow a 16 character (or any multiple of 8) string, without a comma such as "1234abcd5678efgh".  I suspect this is not your intention.  If my suspicion is true then the + operator isn't even necessary and you could use this regex:
^[0-9a-zA-Z]{8}(,[0-9a-zA-Z]{8})*$
to strictly allow a single 8 character string of letters/numbers or a comma separated list.  If the original intent of the + operator was to ensure a value was entered in the field, I would suggest making the attribute mandatory instead.