Does your total economic ouput decline or just your treasury. Because both Republic and Democracy add a significant amount of raw gold to your output, but then also deduct gold for upkeep, it may appear as if you're much worse off than before. However, in most cases you're actually producing a lot more -- this is usually most apparent in terms of tech research. For instance, a plausible example could be: you start your revoultion with 8 turns to go on Feudalism and a slight surplus each turn; you become a republic and suddenly you're running a large deficit - but, you may notice that Feudalism is now only 5 turns away; if you adjust your tech slider so that Fedualism is again 8 turns away, you find that you're enjoying a larger surplus than you had before, even though you're now paying gold for army upkeep. If the above example doesn't resemble your experiences, then my guess is that either (1) you've got a very large standing army, or (2) your empire isn't ready for republic (are their roads on every tile that a citizen is working?). Hope that helps.
Catt