First, be aware the scanning an entire genome for motif occurrences is a difficult statistical problem. It is addressed by the "Futility Theorem"
( Wasserman WW, Sandelin A. Applied bioinformatics for the identification of regulatory elements. Nat Rev Genet 2004;5:276-87.). The statistical power to identify biologically relevant motif matches depends on the information content of the motif and the quality of the background model. If the motif is short, or not very distinctive, there simply may not be the statistical power to distinguish random matches from biologically relevant ones. Consider this: in a 1GB genome there will be roughly 15,000
perfect matches to an arbitrary motif of length 8,
entirely by chance. For FIMO, a perfect match is a perfect mach, so the perfect matches that occur by chance, will vastly outnumber the perfect matches that are "biological". On the other hand, in the same genome you wouldn't expect any perfect matches to a motif of length 12 to occur by chance, so you might have a shot at spotting the biologically active matches. This is just a limitation of using sequence similarity to identify motif occurrences.
Finally, in you post you mentioned that you are using a uniform background model. FIMO's statistical power depends critically on how good the background model is. If you are scanning a whole genome you should probably use the actual genome nucleotide frequencies for the background model. This is admittedly a compromise since the frequencies may vary widely by region, but it's probably the best you can do given FIMO's simplistic background model.