The gemara tells about a civil war between the kings that descended from the chashmonaim when they were trying to capture Yerushalyim and were advised to send a pig up the basket that we used to import the korban tamid. During that period there was no wheat or barley anywhere in the vicinity of Yerushalayim. The Maharsha explains that they were making a concerted effort to be mevatel the korban tamid, omer and shtei ha'lechem. The gemara tells that Mordechai was able to figure out how to communicate with a mute person who was able to tell him through sign language where there would be hidden areas that the troops did not destroy from which they can bring the korbanos. To put things in historical perspective, the chanuka story occurred 206 years before the destruction of the 2nd beis hamkidash. The chashmonaim were all killed out by Herod who took control 103 years before the destruction of the beis hamikdash (avoda zara 9a). It would seem that this story was at the end of the chashmonaim reign - approximately 110 years or so before the destruction. This is almost 100 years after the chanuka story and over 300 years after the purim story (2nd beis hamikdash stood for 420 - גדול יהיה כבוד הבית הזה האחרון מן הראשון).
Rashi writes that Mordechai mentioned in the gemara is the same Mordechai from the time of achashveiros, who was also called פתחיה in the mishna in shekalim and בלשן in nechemia. Tosafos says that it would be strange to suggest that he lived so long and therefore writes that people who were appointed to leadership due to their knowledge and intellect were named after Mordechai. The Ya'avetz supports Rashi - Is it so strange to say that yiras hashem increases lifespan and posits that in the generation of the שיורי בית ראשון, those who remained from the first beis hamikdash, this wasn't such an anomaly.
It seems to me that the biggest problem with suggesting that it was the same Mordechai is that we usually assume that by the time of the chanuka story there were no nevi'im left around. It certainly seems this way from Rashi in Ta'anis 28b who explains that Hallel on chanuka is called a d'oraysa because it was included in the original takana of the nevi'im (mentioned in arvei pesachim) to say hallel every time the Jews are saved from danger. Rashi seems to be okay with takanas nevi'im being called d'oraysa but is troubled that there were no nevi'im at the time of chanuka. To answer this Rashi explains that the framework of saying hallel on being saved from and existential threat to the nation was instituted hundreds or even thousands of years before the chanuka story - just that the chachamim at the time considered this the miracle of chanuka to fit that framework. Yet, we know that Mordechai was from the list of 48 Nevi'im as rashi writes in megillah and together with Esther wrote the Megillah.