Yeah, that's what I was suspecting when I changed the criteria field - a date formatting issue. VBA always expects dates to be in american format.
Anyway, with this new criteria field (a text type one), everything works fine, once this field also has unique records. From now on, I'll have to use:
DELETE * FROM <table_name> WHERE <field_name> = #" & Format(Regional_format_Date, "mm\/dd\/yyyy") & "#
Thank you both of you, pr2-eugin and spikepl. Your help was more than precious.