* Front month hits five-week low, closes below support * Spring weather finally arrives in much of the country * EIA sees 2013 gas output up 1 pct from 2012 record high * Coming up: Reuters natural gas storage poll Wednesday By Joe Silha NEW YORK, May 7 (Reuters) - U.S. natural gas futures ended lower on Tuesday for a second straight day, with moderating weather forecasts and tapering demand driving the front-month contract below technical support. After blowing through minor support at the 20-day and 40-day moving averages over the last week, chart traders said Tuesday's weak close broke support in the $3.94 per mmBtu area, the 38.2 percent Fibonacci retracement of the move up from the February low of $3.125 to last week's high of $4.444. "I'm not ready to throw in the towel on the move up, but this may be a sign that we're going to test further support points," said Dean Rogers, technical analyst at Kase & Company. Rogers sees the market trading in a wide range for at least the next few weeks, with $3.63 marked as the level that prices must hold to avoid sinking into possible bear market territory. While the market is oversold and could bounce ahead of Thursday's weekly inventory report, traders worry that record high net long positions held by speculators could lead to a sharp sell-off if new length rushes to cash out. Front-month gas futures on the New York Mercantile Exchange ended down 9.1 cents, or 2.3 percent, at $3.92 per million British thermal units after slipping to near a five-week low of $3.916 at the floor trading close. The front contract, which hit a 21-month high of $4.444 on Wednesday, lost 2.7 percent last week, its second straight weekly decline after nine consecutive weeks of gains. It is down another 3 percent so far this week. Expectations for a string of above-average weekly storage builds as temperatures moderate have started to weigh on prices. Last Thursday's unexpectedly-large inventory build triggered a 7-percent selloff, the biggest one-day drop in nine months. Traders said moderating weather forecasts have been making previously bullish traders nervous following a cold winter and chilly spring that whittled down record high storage and drove prices up more than 40 percent from the mid-February lows. While there are still below-normal temperatures in the forecast, particularly for Texas and the Southeast, traders noted normal highs are on the rise as summer approaches and below-normal readings in May are not likely to trigger much heating or cooling load. Some traders expect gas prices to remain under pressure, at least until homeowners and businesses crank up air conditioners. The National Weather Service eight-to-14-day forecast on Monday called for above-normal temperatures in the West and Northeast, with below-normal readings in Texas and the Southeast. Seasonal temperatures were expected elsewhere. ANOTHER BIG INVENTORY BUILD EXPECTED Last week's build was only the third injection of the stock building season, but it did exceed market expectations and prices fell sharply immediately after the report. U.S. Energy Information Administration data last week showed total domestic gas inventories had climbed to 1.777 trillion cubic feet, about 118 billion cubic feet, or 6 percent, below the five-year average. That deficit is likely to shrink in Thursday's report. Injection estimates range from 58 to 92 bcf, with most in the high-70s. Stocks rose 30-bcf during the same week last year, while the five-year average increase for that week is 69 bcf. PRODUCTION CLIMBS DESPITE FEWER RIGS Baker Hughes data Friday showed the gas-directed rig count fell last week to an 18-year low of 353. Drilling for natural gas has mostly been in decline for the past 18 months, dropping some 62 percent since peaking in 2011 at 936, but so far production has not slowed much, if at all, from the record high hit last year. The EIA on Tuesday raised its estimate for domestic natural gas production in 2013, expecting output this year to be up about 1 percent from 2012's levels. If realized, it would be the third straight year of record production.