Why did the red colour in a flame test for strontium disappear and appear again on longer heating?
Good, careful observation! Here's my assumption of what happened: 


The $\ce{SrCl2}$ solution on the wire boiled violently, releasing a large amount of the salt into the flame.
Some remaining anhydrous $\ce{SrCl2}$ stuck to the nichrome after all water boiled off, and melted when the wire reached ~$\pu{874^\circ C}$, coating the loop with a thin layer of the salt.
Additional heating, after melting the salt, went into raising its temperature until it approached the boiling point, ~$\pu{1250 ^\circ C}$. Nichrome can withstand ~$\pu{1400 ^\circ C}$ before melting, but you don't even need to reach the b.p of $\ce{SrCl2}$ to have a bit evaporate and color the flame. Ergo, the flame turned red again.


By the way, this implies you could melt $\ce{SrCl2}$ in a ceramic crucible, insert two nichrome wires connected to a battery, and electrolyze the molten salt to see a bit of strontium (which will catch fire as soon as it rises to the surface, with its characteristic flame color). Do this only under a teacher's supervision.