The Baggies have only won one of 12 league matches so far, drawing seven and losing four to leave them in 22nd place on 10 points.
They were punished for a characteristically sluggish start at Deepdale. Emil Riis scored after seven minutes, the seventh time in 12 league matches Bruce's side have conceded the opening goal inside the opening quarter of an hour.
Bruce accepted his side's record of falling behind early is "ludicrous" - but vowed to fight on if the axe doesn't fall before Saturday's meeting with Luton.
Preston boss Ryan Lowe, whose team climbed four places to 11th following a first home win this term, came to Bruce's defence, calling the former Manchester United defender a "top guy and a top manager".
Bruce, however, concedes his future is out of his hands. West Brom mustered 18 shots against Preston but created only a handful of clear openings.
"We are all judged on results and they haven't been good enough," said Bruce, whose side have won only one of 12 Championship fixtures this term. "I will do my utmost to turn it around.
"I still believe we are capable of going on a run with the players we have - but at the moment, everybody is finding it tough.
"That [my future] is for other people. I hope [I will still be in charge at the weekend], I still think I am the right one to turn it around.
"I have done it before, especially at this level, I am convinced [I am the right man].
"I don't give up, not when it is tough. I don't have to do it. But I still get up in the morning and want to come to work.
"It still burns inside me, especially when it is like it is at the minute.
"But I hope I am given the time. If not, I fully understand I haven't been able to arrest a slide that has gone on for two-and-a-half years."
Preston had chances to extend their lead before half-time, Ali McCann striking a post and Sean Maguire fractionally wide from distance.
West Brom stepped up a gear after the break and it needed a fine one-on-one save from Freddie Woodman - who recorded a ninth clean sheet this term - to deny Karlan Grant an equaliser.
"I always believe we will score goals because of the way we play and we should have been 3-0 up at half-time," said Lowe, whose side had scored only once in six home matches prior to this contest.
"We could have scored more but we got one and got three points and can build on that.
"It isn't relief, because we are doing alright.
"The performances have been outstanding, we've just not been getting three points."
On opposite number Bruce, Lowe added: "He is a top guy and a top manager and sets his teams up well.
"In fairness, they should have scored a couple of goals - but we were solid and resolute.
"Steve Bruce is a fantastic manager and long may it continue."