I wondered what's the average, and maybe the highest shared cM you've seen with a relative from two or three centuries back?
MRCA 3G grandparents, born c 1800, 4 matches share 55 cMs across 6, 47 cMs across 3, 28 cMs across 1, 20 cms across 1 segment, 4th cousins
MRCA 5G grandparents, born c 1733, 2 matches share 20 cMs across one segment, 6th cousins
MRCA 4G grandparents, born c 1776, shares 20 cMs across one segment, 5th cousins
Plugging 45 cMs into dnapainter suggests a very wide range of relationships, as close as 3rd cousin, as distant as 8th cousin or further.
Use the new filters if you are at Ancestry to look at all your matches between given ranges.Of my matches, those in the region of 40 cMs - 50 cMs are 3rd or 4th cousins, none more distant. Only one is unconfirmed because he has no tree, but using shared matches I know which line he belongs to, likely to be 3rd to 4th cousin as well.
So, speaking from my experience alone, I would think that 45 cMs is a lot closer than you are suggesting.
But it doesn't depend upon how many centuries ago, but how many generations ago the MRCA is on both lines. A family where the mother had several children from her 20s to her 50s, and where the oldest and youngest child followed the same pattern, there could be between 2 and 5 generations of her descendants born in one century.
If the pattern repeats itself you are unlikely to be a DNA match with any of the oldest group from 1800, whereas you could be DNA match with the youngest group from a lot earlier, even 1600s.
E.g. Tester born 1950, grandmother born 1910, 2G grandmother 1870, 4G grandmother 1830 etc
E.g,Tester born 1950, grandmother born 1850, 2G grandmother 1750, 4G grandmother 1650 etc.
Regards Margaret