Keane succeeded Jim Magilton as manager in April 2009 and won his first two games with the club at the end of the season.
However, the club then made their worst ever start to a campaign in 2009/10 - going 14 league matches without a win.
"It took him a long time to get that first win," said Holland.
"He turned it round a little bit. The start of this year it looked like things were going in the right direction - good start to the season, into the play-offs - but obviously things have tailed off in recent weeks."
First-team coach Ian McParland is to take temporary charge for the FA Cup tie at Chelsea whilst a permanent replacement is sought.
Holland played alongside Keane for the Republic of Ireland
The first leg of the Carling Cup semi-final with Arsenal follows, but Holland says the main aim for this season will be staying in the Championship.
"They need some stability at the football club," he said.
"The last two managers had a couple of years each and now it's a rebuilding job.
"The ultimate aim has to be getting back to the Premier League but at the moment, you look at the position, three points off the relegation zone, the key now is staying in the division this year and rebuilding next.
"It's not without a chance, but it would be unrealistic to think you can turn it around over night and get into the play-offs."
Curbishley a candidate
Alan Curbishley is spoken of as being a potential candidate to take over from Keane.
"Alan is a very good manager and I enjoyed playing under him (at Charlton)," said Holland. "Very good on the training ground, very methodical.
"I think he's a terrific guy and I think he'd do very well at Ipswich.
"He always said he'd only take a Premier League job, but Ipswich is a very big club and a big, big job.
"It's a terrific place to work, a great training field, a good squad, has potential.
"The only way is up and you never know, he may well fell it's a job worth taking."
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