Bonferroni correction, as you have observed yourself, is very conservative, resulting in a lot of false negatives. Literature and the internet are full of references on this matter but here is a ref in the bioinformatics context.

Any idea why this is happening? For example, I got 1064 significant probes from raw p-values, but only 18 from Bonferroni correction, and 1052 from FDR correction.

Is this a Fisher/Chi2 pval? Anova? What is the raw data input? Is Bonferroni the right correction? Assuming its NGS-reads, this points to very similar values you're comparing. Is there a depth imbalance? Is the depth low? If you make a histogram of pvals before FWER(FDR) correction, are they 'quantized' ?