I had a similar problem recently, and wrote a library to help solve it: pdfquery.
PDFQuery creates an element tree from the PDF (using pdfminer, with some extra sugar) and lets you fetch elements from the page using JQuery or XPath selectors, based mostly on the text contents or locations of the elements. So to parse a table, you would first find where it is in the document by searching for the label:
label = pdf.pq(':contains("Name of your table")')
left_corner = float(label.attr('x0'))
bottom_corner = float(label.attr('y0'))
Then you would keep searching for lines underneath the table, until the search didn't return results:
page = label.closest('LTPage')
while 1:
row = pdf.extract( [
('column_1', ':in_bbox("%s,%s,%s,%s")' % (left_corner+10, bottom_corner+40, left_corner+50, bottom_corner+20)),
('column_2', ':in_bbox("%s,%s,%s,%s")' % (left_corner+50, bottom_corner+40, left_corner+80, bottom_corner+20))
], page)
if not row['column_1'] or row['column_2']:
break
print "Got row:", matches
bottom_corner -= 20
This assumes that your rows are 20 pts high, the first one starts 20 pts below the label, the first column spans from 10 to 50 points from the left edge of the label, and the second column spans from 50 to 80 pts from the left edge of the label.
If you have blank lines or lines with varying heights, this is going to get more annoying. You may also need to use the merge_tags=None option to select individual characters rather than words, if the entries in the table are close enough to make the parser think it's just one line. But hopefully this gets you closer ...