Does upgrading the airport card to "n" improve the reception?

Of course you have already accessed your wireless router configuration and tried different "channels" and a longer Threshold.

The "Early 2009" & "Late 2009" Mac mini models support 802.11n, but earlier models do not, a revised antenna configuration is required to support the card.

802.11n does provide a somewhat longer range and by changing broadcast bands is can overcome some interference difficulty. Other5Ghz wireless devices (mobile phones) might still cause problems.

If this answer was helpful please remember to return and mark it Accepted.