The 50-year-old sprung to the Rhinos' rescue last year but an initial short-term deal evolved into a contract until the end of 2025 after the squad saw a vast improvement under his charge.
After two campaigns without a post-season optimism now abounds following the signings of Fiji's Maika Sivo from the Eels, former Broncos and Titans Samoa international Keenan Palasia, and Great Britain caps Ryan Hall and Jake Connor, but Arthur is reluctant to give assurances over the length of his tenure.
"I love the club and the players have been great, but if you want me to be honest, it's tough being away from your family," said Arthur.
"I've got two boys back in Australia (NRL players Jake and Matt) who I'm not going to see for 11 months, and it's just how you handle that."
Arthur said he would not have agreed to his current, extended deal if his wife and daughter had not committed to settling in England with him ahead of the new Super League season, which gets under way next month.
"They came over for a couple of weeks, then they went back and forth, which was OK but still a struggle for me," he added.
"I said to my wife, I'm not staying here if they don't come over. I didn't want to put that pressure on them but I just couldn't do it."
Arthur, who says he is comfortable about putting the issue on hold until the end of the upcoming campaign, is also clear that his longer-term ambitions reside back Down Under following his previous decade-long stint in charge of Parramatta Eels.
"It's a good experience, and I'm so grateful for the opportunities I've been given," added Arthur.
"It's changed me a little bit and I reckon it's helped my coaching, having to get a team ready in six weeks.
"I feel like I still want to go back and coach in the NRL at some stage, but I feel like I'll be more equipped for it. My family's got different experiences out of it as well, and I've totally enjoyed my time here."
