Thanks Juliette. Yes, it helps.
I will check out Better WP Security and look at adding it since I'm having all these issues. FYI, I just got this response from Hostgator Security:
"Unfortunately it appears that there were some malware injections that had evaded our previous detection techniques and therefore remained on the account since the last cleaning. At this time we have gone through and removed them."
So perhaps this is all related to the hack I experienced a few months ago and hopefully it will now all stop.
Debbie