We analyse U-Pb in zircons here and our data of 202 Hg is starting with 30000 cps and decrease 1000 per hour. We changed filters, gas, clean the station and heat the gold...nothing worked.
Without more details, that question is really hard to answer. From your question, I assume you have gas line filters in place - is that for the cell gas (He?) only, or also on the plasma gas line (Ar)?
If you measured "dirty" samples with this system before, like metallic samples, sulfides or other sources of high Hg and Pb, significant contamination might have accumulated on all surfaces exposed to the aerosol. This includes, besides the sample camber and sample holder, also all the tubing, valves, and tubing connectors after the LA cell. Strong contamination can take very long (days, weeks) to wash out. Some people have success with regular change of the tubing.
If your gas supply is contaminated, Hg will also have accumulated in all the gas lines before the filters. This would need to wash out even after changing to "clean" gas. The filters only have a limited capacity.
You mention "heat the gold" - where in the setup do you have a gold filter in line?
And finally: many labs are struggling with this problem, and some fail to ever get rid of the Hg background. Many theories for the source of the Hg signal have been suggested, but it seems that what works for one lab, does not necessarily solve the problem for others. If you are "only" measuring zircons, and if these aren't extremely young, it might be enough to just rely on 206Pb and 207Pb, and not try to measure 204. You can attempt an age-based common lead correction for discordant ages instead.
To follow-up on Martin's response, I should add that, depending on what type of ablation chamber you have, you should be able to "bake" the Hg out by removing the cell and sample holder(s) from the laser and heating them up in an oven at reasonably high temperatures (