Hi Starr 
- your melatonin thread seems like yesterday, but I think that’s cos I’ve been trying it… Short indirect answer to your question: Looking at what a lot of others have written here, I’d say: Yes, it does stop working for some.
Pardon me for “analyzing” what you’ve written, that’s what I do with my blog/diary…: Based on what you’ve written in former posts I’d think it didn’t help you that long, since 2x25mg didn’t help and 2x50mg only a bit. That was about two months after starting: July 2020? And in Dec 2020 you already wrote that it is not helping any more, which you probably realized quite a time before. If that all fits together, it was less than half a year. And you even needed to increase from 100mg to 125 - Was it praps your adamant doc’s enthusiasm that made you think it worked 
So it doesn’t sound at all worth it to me. What you could try to repeat the effect is to stop it for a few months and then start afresh, going up quickly (inside of weeks) from 2x25 to 2x125mg in cycles…
Out of interest I’ve had a look at a third of the 345+ posts here on savella and found the following:
Summary: For some it’s a miracle, even after 2… years (dee_B, last seen 2014, Luna01, renewing profile 2015), which they feel everybody should take (them and Suzyb! ;-)), some have side effects but the body got used to most of them or the benefits outweigh them, and quite a lot stop it early or after a few months because of bad side effects.
Cutting the price (no idea if this is realistic): I can't afford my Savella - #2 by Laura_Weir, Anyone try "Milnacipran" marketed under the brand name of "Savella"? - #4 by Jackiem, Just started taking Savella - #2 by Luna02, https://forum.livingwithfibro.org/t/savella/5144/2: The cost varies so much even in the same area that the best way to find out is to call several pharmacys.
https://forum.livingwithfibro.org/t/savella/5144/3: My scrip usually cost me about $50 a month but it also depends on insurance because it was less with my other insurance I had before.
Savella? - #4 by ShanesGirl4Ever With my insurance it was under $10.
Not working any more (Rebecca, niteowlie): What do you do when it gets really bad?, Sick & tired of being sick & tired - #2 by Rebecca
Savella - #5 by niteowlie, What pain medication do you take? - #24 by Rebecca
You yourself:
"Cymbalta? Lyrica? Gabapentin? I'm confused - #19 by Starr1 Dec, where you also mention starting melatonin, Nervous about returning to work full time - #3 by Starr1 up from 2x25mg to 100mg, after it had not been working at 25mg and only a bit at 2x50mg.
Wonderful first, but stopped helping after 4 months (12mamabear): Have you found Savella effective? - #10 by 12mamabear, Wonderful first, but stopped helping even on the highest dose paid for (12mamabear): Have you found Savella effective? - #16 by Snooty
For Starr (!) it was too expensive: Cymbalta for fibro pain - #6 by Starr
Taken for a year, not working (Rebecca too…): What do you do when it gets really bad? - #9 by Rebecca
Savella with Lyrica after 8 years stopped working Just started taking Savella - #6 by witsend
Increasing from 50 after not working any more: Savella increase?
https://forum.livingwithfibro.org/t/savella/1095/2: once the side effects went away so did the drugs effect in my body (MoMerrell)
100mg is the highest safe dose(?) Savella? - #15 by Laura_Weir