NEW YORK (CNN/Money) - Shares of United Airlines parent UAL soared Monday as investors were cheered by a new cost-cutting deal with the airline's pilots, but analysts still said they think there is a good chance the No. 2 air carrier will fly into bankruptcy court later this year.

Shares of UAL (UAL: up $0.76 to $3.32, Research, Estimates) were about a third higher in midday trading Monday.

The airline is seeking $5.8 billion in cost cuts from its unions in an effort to win $1.8 billion in federal loan guarantees. It has about $875 million in loans and payments on guaranteed debt due in the next four weeks, and without the guarantees, it has warned, it could file for bankruptcy court protection before the end of the year.

The company was able to make $40.5 million in scheduled debt payments this past Friday without using a grace period or seeking an extension from lenders. The company is talking to banks that hold $300 million due Nov. 17 about a possible extension, said United spokesman Joe Hopkins.

"We are pursuing getting the labor agreements in place and getting the guarantees as soon as we can. We are also talking about the deadline and could it be relaxed a little," said Hopkins.

The tentative agreement with the pilots will save the company an estimated $2.2 billion over the next 5-1/2 years as pilots take about an 18 percent pay cut, according to Steven Derebey, a United 767 pilot and spokesman for the Air Line Pilots Association. But this labor agreement was seen as the easiest one to reach, as ALPA had agreed to a previous 10 percent wage cut package earlier in the summer when the two other major unions -- the International Association of Machinists and the Association of Flight Attendants -- balked at deals.

"Most of the pieces of a [new] agreement were taken right from agreement we had," said Derebey. "We increased some of the numbers, but the overall framework of the first agreement was valid."

Talks were held over the weekend with some other union groups but not the IAM, which is expected to resume talks early this week. The airline announced an agreement early Monday with the Transport Workers Union, which represents about 30 weather forecasters. A spokeswoman for the AFA said that its negotiators were at the table with management until late Sunday night and would be back at talks Monday.

While neither United nor AFA and IAM officials would comment on a possible deadline for any other agreements, the pilots' spokesman said the other deals should come soon.

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"We're very confident that everyone is going to reach an agreement, and confident they'll reach an agreement this week," said Derebey.

But analysts said they want to see an agreement with the other unions, particularly the IAM, before they'll start to believe the airline might still avoid bankruptcy, and even then they said there's a chance the Airline Transportation Stabilization Board, which decides upon loan guarantees, could reject United's request. Ray Neidl, analyst with Blaylock & Partners, puts the chance of a bankruptcy filing at about 60 to 70 percent, while Jim Corridore, airline equity analyst for Standard & Poor's, also puts the chance at 70 percent.

"The pilots were on board before all the bankruptcy talk. It is probably the easiest labor pact to get," said Corridore. "I still think the bankruptcy risk at United is very high until I hear two things -- an agreement with the machinists and some positive feedback from the government."

Neidl thinks that the airline will be successful negotiating an extension of the $300 million in bank debt due Nov. 17. But he said he doubts that the $575 million in bonds secured by aircraft that is due in early December will be far more difficult to delay.

"Everyone is working very hard now to avoid the bankruptcy. But you could have everyone on board but one entity, and that can gum up the works," Neidl said.

United's Hopkins wouldn't comment on the airline's chances of avoiding a bankruptcy filing except to say that the company is doing everything it can to avoid such a filing.

"Bankruptcy is not a foregone conclusion," he said.