Using xtlogit with fe and bootstrap SEs, losing almost all of my observations

[Anna Hooks]

I'm currently using xtlogit w/ fixed effects and SEs, and it is dropping almost all of my observations. However, when I run xtscc or xtreg with the same fixed effects and lag(4), it is not dropping observations. Many of my respondents reported the same answer across my included time periods, ie said yes all four years, and I'm wondering if having limited variation is impacting this. Here are the two models I'm running, with the first dropping out almost all observations:
xtset ID0 year
xtlogit flc shortage_yesno_ i.year, fe vce(bootstrap, reps(100))
xtscc flc shortage_yesno_ i.year, fe lag(4)

[Jeff Wooldridge]

Anna: With so-called fixed effects logit — actually a conditional MLE — only units with some time variation in y(i,t) contribute to the estimates. This actually makes sense because all zeros or all ones are explained by the unobserved effect when x(i,t) is allowed to be correlated with c(i). With the linear model, they still contribute if some x vary across time. In the linear case, Stata doesn’t give you a breakdown of which observations are effectively being dropped.

[Jeff Wooldridge]

As a follow up, you shouldn’t be using xtscc with T = 4. Just use xtreg either fe and cluster by id.