* Weekly EIA stock build falls short of expectations * Weather outlooks mixed for remainder of April, early May * Nuclear power plant outages remain below average * Coming up: Baker Hughes rig data, CFTC trade data Friday By Joe Silha NEW YORK, April 25 (Reuters) - Front-month U.S. natural gas futures pulled back from early highs but still managed to eke out a small gain on Thursday, underpinned by a smaller-than-expected weekly inventory build that was well under the historical average for that period. It was the first gain for the front month in four sessions. Data from the U.S. Energy Information Administration showed total domestic gas inventories rose last week by 30 billion cubic feet to 1.734 trillion cubic feet. That was below the Reuters poll estimate of 32 bcf and well below the five-year average increase for that week of 50 bcf. "The (EIA build) number was slightly bullish - it missed expectations by 2 bcf and it was below the seasonal average - but people are looking forward to storage injections in early May when we should see much bigger builds as temperatures moderate," said Gelber & Associates analyst Aaron Calder. Front-month May gas futures on the New York Mercantile Exchange, which expire on Friday, shot up 8.5 cents, or 2 percent, to $4.251 per million British thermal units right after release of the EIA data at 10:30 a.m. EDT (1430 GMT). But the front contract ended the session up just 0.1 cent at $4.167. Cold late-winter weather, a chilly spring and above-average nuclear plant outages put a huge dent in record gas inventories and helped drive prices up 40 percent since mid-February. But despite lingering cold this week and prospects for another light storage build in next week's report, some said the upside for gas futures seemed to be stalling after nine straight weeks of gains, particularly with milder weather on the horizon. The front contract, which hit a 21-month high of $4.429 late last week, had lost 5.5 percent in the previous three sessions, breaking and closing below trendline support on Wednesday. Chart traders said the break down could be a bearish sign and set up a test of better support in the $4.12-4.13 area, the 20-day moving average and the 23.6 Fibonacci retracement of the move up from the $3.125 February low to last week's peak. Matt Smith, commodity analyst at Schneider Electric, pegged major support in the $3.93 area, which is the 38.2 Fibonacci measurement and the front-month high in 2012. Some said a close below that level could herald the end of the bull market, at least until hotter weather kicks up air conditioning loads. Forecaster Commodity Weather Group expects temperatures in the central U.S. and Southeast to cool to below normal next week, then moderate to mostly seasonal levels in the 11- to 15-day time frame that should again slow demand. ANOTHER LIGHT INVENTORY BUILD This week's storage injection was only the second of the stock building season, which started about three weeks later than expected due to an unusually cold spring. The weekly build widened the deficit relative to last year by 13 bcf to 807 bcf, or 32 percent below last year's record highs at that time. It also increased the shortfall versus the five-year average by 20 bcf, leaving stocks at 94 bcf, or 5 percent, below that benchmark. Chilly weather this week is expected to continue to slow inventory builds and drive stocks further into deficit relative to the five-year average in the next EIA report. Early injection estimates for next week's report range from 15 to 40 bcf versus a 31-bcf build during the same week last year and a five-year average rise for that week of 67 bcf. OUTPUT NOT SLOWING MUCH YET Traders were waiting for the next Baker Hughes drilling rig report on Friday. The gas-directed drilling rig count rose slightly last week for the second straight week, stirring expectations that higher gas prices may be tempting producers to hook up more wells. While the gas rig count is hovering just above a 14-year low of 375 posted two weeks ago, production so far has not slowed much, if at all, from the record high hit last year.