Node.js file write in loop fails randomly

Here is my code :

function aCallbackInLoop(dataArray) {
        dataArray.forEach(function (item, index) {

            fs.appendFile(fileName, JSON.stringify(item) + "\r\n", function (err) {
                if (err) {
                    console.log('Error writing data ' + err);
                } else {
                    console.log('Data written');
                }
            });
        });
    }

I get random errors :

Data written
Data written
.
.
Error writing data Error: UNKNOWN, open 'output/mydata.json'
Error writing data Error: UNKNOWN, open 'output/mydata.json'
.
.
Data written
Error writing data Error: UNKNOWN, open 'output/mydata.json'

The function (aCallbackInLoop) is a callback for a web-service request, which returns chunks of data in dataArray. Multiple web-service requests are being made in a loop, so this callback is perhaps being called in parallel. I doubt it's some file lock issue, but I am not sure how to resolve.

PS: I have made sure it's not a data issue (I am logging all items in dataArray)