The definition of a perfectly balanced string can be simplified to "any even-length string where the character frequencies in the first half are the same as the second half."
Since there are only (26) letters, we can precompute a prefix-sum array (P_c) of frequencies for each letter (c), where (P_c[i]) stores the frequency of letter (c) in (S_{1..i}). This will let us obtain the frequency of any letter (c) in any substring (S_{a..b}) in constant time, using (P_c[b] - P_c[a-1]).
For each query substring (S_{l..r}), there are two possible split-points to check in the middle. Let (m = \lfloor(l + r)/2\rfloor). We can first compare the frequencies of (S_{l..(m-1)}) with (S_{m..r}), then compare the frequencies of (S_{l..m}) with (S_{(m+1)..r}). If in either comparison we find that the frequencies differ by exactly (1) letter between the two sides, then (S_{l..r}) is almost perfectly balanced.