What makes you think that the power is dropping?
Are you taking the indication of power from the radio itself, or from an external power meter (maybe one built into the tuner you're using)?
Taking the problem in two sections, if the radios own internal metering is suggesting that the power is lower than normal
then you cannot have a correct match, there is still some inductive or capacitive reactance present that is causing the radios internal coupler to either mis-read, or else the radio is 'rolling back' its output power to protect itself from a mismatch.
If it is a mismatch causing the radio to reduce its output power,
then either you have not tuned/matched the system correctly, or, the device that you are measuring the SWR on the system is not calibrated correctly.
If we now look at the problem another way, if the internal power metering in the radio is saying that all is OK i.e. you are seeing 100% power on the radios display, but the external SWR/power meter is suggesting that the power is lower than normal, then either the external meter is incorrectly calibrated, or else you are using a patch lead that is very lossy or perhaps damaged.
Looking at your quote: "the power drops from the radio a bit", I'm wondering just how much is "a bit"? Are we talking 10-20 watts, or just a couple of watts?
Most RF power meters tend to only have an accuracy of about plus or minus 10% of full scale deflection, and many RF power meters can be out by as much as about 15-20% at midscale. Not all, just some.
Another effect that can be observed is that the accuracy changes with frequency, normally due to imbalances creeping in on the coupler itself. An SWR/power meter may indicate 110 watts at 1.9MHz, 100 watts at 14.150MHz, and 80 watts at 29MHz, all for the
same input power level!
What I would say is that if the radio itself indicates 100% power, and when your SWR meter indicates little or no reflected power all seems well and folks can hear you OK, then don't worry about it.
The further any antenna deviates from its 'ideal' feedpoint impedance, and the more heavily you have to rely on the capacitors/inductors in a tuner to obtain a good match (for 'good match' read 'fool the radio into thinking all is well), then invariably the greater will the losses become. Many base loaded mobile antennas are only around 1%-3% efficient, so your 40m windom running on 80m would appear to be almost super conducting by comparison!
73, Mark.