Shares of Republic Airways Holdings Inc. have been skimming treetops lately, falling within pennies of their 52-week low of $4.43 per share as the once contract-only airline struggles with rising fuel costs for Frontier Airlines, the scheduled carrier it acquired in 2009.

Indianapolis-based Republic stock closed Tuesday at $4.51 a share with the company struggling to cut expenses this year by $100 million, “which if successful will allow Frontier to have a sustainable business model,” CEO Bryan Bedford told analysts last month.

Bedford and his management team are still trying to prove to critics that they have what it takes to compete in the cutthroat scheduled airlines segment. It didn’t help that former Frontier CEO Sean Menke, credited with guiding the Denver carrier through bankruptcy, resigned from Republic last year for personal reasons.

Republic outbid much bigger rival Southwest Airlines to buy Frontier in a rare defeat for the Dallas-based carrier, which has been gunning hard against Frontier in key markets such as Denver.

Before buying Frontier—along with Milwaukee-based scheduled carrier Midwest Airlines in 2009—Republic since the 1970s had exclusively flown smaller, regional jets on contract for scheduled carriers.

Contract flying is not as vulnerable to spiking jet-fuel costs, as the brunt of such expenses are borne by the scheduled carrier that hires Republic. The contract flying unit produces “reasonably predictable margins” in the 7.5-percent to 8.5-percent range, Republic executives told analysts recently.

But Frontier’s fuel expenses during the first quarter of 2011 were 24 percent higher than the same period in 2010, representing a $30 million increase.  Republic recently said it is projecting further rises in fuel prices for the last three quarters of this year, or about a $90 million increase in expenses.

Republic has responded with a modest fare increase and by accelerating its plans to take smaller, Embraer jets out of Frontier’s fleet and put them into contract flying for Delta Air Lines.

Bedford told analysts last month: “We are going to go back and develop a new business plan for Frontier, which lowers its costs, and will allow it to produce positive cash flow at current fuel costs.”

Frontier and other airlines have been able to mitigate much of the impact of higher fuel costs thanks to stronger demand and seven industry price hikes so far this year, but “pricing is not keeping pace with the rise in fuel prices, adversely impacting earnings,” Goldman Sachs analyst Min Park wrote in a report on Republic.

Meanwhile the company is fighting continued losses in Milwaukee, the former home of Midwest, which was rolled into the Frontier brand.

One way to generate more cash is the potential to refinance short-term loans, which could produce up to $80 million in new cash for Republic, its chief financial officer, Tim Dooley, told analysts.

During the first quarter, Republic took a loss of $22.4 million, or 46 cents a share.  The company projects a consolidated second quarter loss, as well.

Shares of Republic closed as high as $9.58 each in November.