R: Need Finite 'Ylim' Values in Function

I'd like to plot the data in data.frame xy for each group (defined by ID). When a year before 1946 is in a group, plot 2 should be executed. When the years are between 1946 and 2014, plot1 should be executed.

My problem: This works fine without NA values, but as I have data gaps I rely on NAs to define these data gaps. This is why I get an error: error in plot.window(need finite 'ylim' values). I tried to put finite=T in plot1 at the y-axis but this gives a subscript out of bounds error. Is there a way I could solve this and that the graphics are correctly plotted?

In the following is my code: It is long but most of the code consists of plot() options on which I rely.

# read in sample data and split it up by group (defined by ID)
xy <- data.frame(NAME=c("NAME2","NAME2","NAME2","NAME2","NAME2","NAME3","NAME3","NAME3","NAME3","NAME5","NAME5","NAME5","NAME5"), ID=c(48,48,48,48,48,32,32,32,32,67,67,67,67),YEAR=c(1981,1983,1984,1988,1989,1984,1984,1988,1988,1899,1933,1948,1958),VALUE=c(0,205,-570,0,-310,-3680,-3680,NA,-3680,0,NA,13,-98))
ind <- split(x = xy,f = xy[,'ID'])

# Plot Scenario 1: if only years between 1946 and 2014 are present for each group do this:
  plot1 <- function(x) {
  fname <- paste0(x[1, 'ID'], '.png')
  png(fname, width=1679, height=1165, res=150)
  par(mar=c(6,8,6,5))
  plot(x = c(1946, 2014),
       y = range(x$VALUE),
       type='n',
       main=x[1, 'NAME'],
       xlab="Time [Years]",
       ylab="Value")
  axis(2, at = seq(-100000, 100000, 500), cex.axis=1, labels=FALSE, tcl=-0.3)
  points(ind[[i]][,c('YEAR','VALUE')], type="l", lwd=2)
  points(ind[[i]][,c('YEAR','VALUE')], type="p", lwd=1, cex=1,   pch=21, bg='white')
  abline(h=0)
  dev.off()
}

# Plot Scenario 2 if years under 1946 are present do this:
plot2 <- function(x) {
  fname <- paste0(x[1, 'ID'], '.png')
  png(fname, width=1679, height=1165, res=150)    
  par(mar=c(6,8,6,5))
  plot(x[,c('YEAR','VALUE')],
       type='n',
       main=x[1, 'NAME'],
  xlab="Time [Years]",
  ylab="Value [mm]")
axis(2, at = seq(-100000, 100000, 500), cex.axis=1, labels=FALSE, tcl=-0.3)
points(ind[[i]][,c('YEAR','VALUE')], type="l", lwd=2)
points(ind[[i]][,c('YEAR','VALUE')], type="p", lwd=1, cex=1,   pch=21, bg='white')
abline(h=0)
dev.off() 
}

# Execute functions
    lapply(ind, function(x) ifelse(any(x$YEAR < 1946 & x$YEAR < 2014), plot2(x), plot1(x)))