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That means your algorithm is "quadratic" in the meaning of how time of work depends on the amount of incoming data.
Since max string length is about 1e6, max number of operations of your algorithm is (roughly) about 1e12. But 1-2 seconds of running example is sufficient (very roughly) only for about 1e7 operations (surely it depends on used language and judge hardware etc).
Therefore I suspect that this problem requires very different solution (maybe almost "linear" in the meaning of time spent).
I could not invent such a solution right now, but it should exist (according to limit of 1000000). Could you find it yourself?
However I did not regard that there are very few different symbols (26)... However you did not check if string could be "palindromed" at all before working with it...