H3 is never going to be a triplet. If just looking at 3J, then it will be coupled to H4 and H8, which would make it a doublet of doublets. This substituted pyrrolizine is a very sterically constricted fused ring; the possibility that you do not observe one of these 3J couplings is not unreasonable. In fact, if your assignments are correct, then you see the same pattern with your H6 protons, with the 2J (geminal) coupling apparent, but only one of the H6 protons showing coupling through to H7.
Remember that in restricted ring systems, it is often possible to see 4J and 5J as well.
However, if you look closely, you will see that the H6 signals are wanting to split into smaller doublets. I'm sure you'd see it if you reprocessed this data using a suitable window function; from the data you've got it looks like it was run on an Avance 500, so using Topspin you could set gb 0.3 and lb -0.3 and reprocess using gfp, or just set lb -.3 and process using efp. Alternatively, as this is a MNova printout, you can use interactive processing to see (using similar parameters)