Santos were beaten 4-3 by Chippa United in the final match of the Promotion Play-off mini-league, which means a new Cape Town team, Chippa, now replace Santos in the top-flight.
"It's a disappointing time for all at this club. But I am not leaving. I would like to stay and help the club win the First Division and get back into the Premiership," Arendse says.
"I am not one of those players who have contracts that state they will leave if the club are relegated.
"I was part of the Santos team that won all those trophies and I am happy to help this team again next season."
This will be good news to the likes of Santos owner Goolam Allie and COO Edries Burton who look set to lose Eleazar Rodgers and Erwin Isaacs.
Talk is that Orlando Pirates want the pair, but KickOff.com has it on good authority that Bidvest Wits are also doing all they can to secure Rodgers.