SINGAPORE (Reuters) - Oil prices nudged higher for a second day on Monday, struggling to end their steepest slump in more than a decade amid robust winter fuel stocks and easing geopolitical and weather risks to oil supplies. NYMEX crude for October delivery was up 15 cents at $63.48 a barrel in Globex electronic trading by 2310 GMT, building on Friday's 11-cent gain and again attempting to halt a $9 collapse in prices over the past three weeks and a near 20 percent reversal since mid-July's record high $78.40 a barrel. From peak to trough, oil prices have fallen by...