Just to hammer the point: You don't measure SWR in SSB mode. Use a carrier mode, CW, FM, AM. Period.
This is not entirely correct. You can monitor SWR in any mode: I've certainly trimmed
my tuner while talking on SSB, even with a conventional SWR meter, by adjusting for
minimum reflected power even when it is jumping around.
With proper equipment that can compare forward and reflected power instantaneously
you can monitor the actual SWR on any mode. There was a simple automatic meter
in QST some years ago using an LM3914 LED bargraph driver that worked with SSB
signals. (The reading was pretty consistent from 5 to 100 watts output.) And any
power meter with a peak reading hold circuit for each channel can compare them
and generate an SWR indication that is pretty consistent.
The point being, of course, that you can measure SWR on an SSB signal as long as
you have equipment that is designed for that purpose.
If you set the forward
sensitivity manually, as with many inexpensive meters, then the varying output in SSB
mode will cause the reflected power, and therefore the indicated SWR, to jump around.
Without knowing what type of meter is being used, we can't really say whether the
observed symptoms are to be expected or not.
But I have seen a few things that can lead to a difference in SWR with changes in the
mode or similar sorts of things. They aren't common, certainly, but they can (and have)
Probably the most common one is harmonic or other spurious outputs. These don't show
up on a dummy load, but will to various degrees with any frequency-specific load like an
antenna. If the transmitter is being overdriven in SSB mode such that the peaks of the
waveform are being clipped, that will generate harmonic output that may not be present
in the CW waveform (especially if the rig is driven to the same output power on an average
reading wattmeter, in which case the finals may be well over driven on SSB peaks.)
The SWR meter will read higher if the antenna has a higher SWR at the harmonics than
at the fundamental.
I had one case where my SWR read higher when I wasn't talking than when I was: that
turned out to be an oscillation in the IF stage about 100kHz away from my operating
frequency. After I adjusted my tuner for a 1 : 1 SWR at the operating frequency, the
spurious read about 2.2 : 1 when I wasn't talking. The amplitude of the spurious signal
decreased as my modulated signal increased, so the SWR really did vary as I talked.
(The fact that the meter indicated output when I wasn't talking was a clue that
something wasn't right.)
You can even have the same problem with a very narrow bandwidth antenna. This most
often appears as an issue limiting the keying rate for VLF stations, but a very high Q
antenna on 80m or 160m might show the same symptoms (or if the tuner is adjusted to
a very high Q setting). Basically the CW signal is at only a single frequency (+/- a few
tens of Hz for keying bandwidth) while the SSB signal is spread out over a 2 kHz range.
With a very high Q antenna / tuner combination the SWR may vary over that 2 kHz
bandwidth, so the SWR will be higher in SSB. Most of us won't encounter such a problem,
however, unless we are experimenting with very small, efficient tuned loops on 80m or 160m.