Is there a minimum variance for metafor::rma.mv()?

Question

I want to run a three-level meta-analysis model of observed data with Measurement as a nested level of Study (independent samples, only source of covariance being the study group measuring them) using the metafor package in R. However, when I try to run rma.mv() on my dataset, I get a warning, copied below:

Warning messages: 1: In rma.mv(data = final, y, v, random = ~1 | Study/Measurement, method = "REML") : There are outcomes with non-positive sampling variances. 2: In rma.mv(data = final, y, v, random = ~1 | Study/Measurement, method = "REML") : 'V' appears to be not positive definite.

All of my sample variances are positive, but due to disease in my sample species naturally occurring at low prevalences, they are very small. Is there a non-zero minimum for variance for this model to fit?

Here is a portion of my dataset as an example:

                    Author            y         seTE Study Measurement            v
1           Author1 (2015)  0.597156000 0.0337653340     1           1 1.140098e-03
2           Author2 (2010) -0.000300000 0.0165236190     2           1 2.730300e-04
3           Author3 (2007) -0.037336000 0.0080100780     3           1 6.416135e-05
4           Author4 (2008)  0.010016000 0.0322690010     4           1 1.041288e-03
5           Author5 (2016)  0.064000000 0.0094868330     5           1 9.000000e-05
6           Author5 (2016)  0.020000000 0.0122065560     5           2 1.490000e-04
7           Author6 (2015)  0.031000000 0.0044721360     6           1 2.000000e-05 

And the relevant part of my script:

model_3 <- rma.mv(data = final,
                  y,
                  v,
                  random = ~1 | Study/Measurement,
                  method = "REML")