Does the problem occur at specific times of the day?

If the problem occurs at specific times of day, it could be that it is dependent on system loading. Typically, peak system loading is at mid-morning and mid-afternoon, and so these are the times when load-dependent problems are most likely to occur. (If your WebSphere MQ for iSeries network extends across more than one time zone, peak system loading might seem to occur at some other time of day.)