One reason you're seeing this "works sometimes and not others" might be that the latest Java 7 update 51 has a new, more restrictive security model. All java applications are required to be "signed". This is extra data provided to the java in your web browser by the hosting website. It helps ensure that the applet running in your web page comes from the source you expect it to be, and not masquerading from somewhere else.
Unfortunately, as applet signing wasn't required, many were not, and Java 7 update 51 is fairly new. Before this, signing was optional, and though well-designed applets by experienced designers and/or Web Operations personel may have done this as a best practice, it simply worked without it. Now it doesn't.
You can downgrade your java, to the last update which does not require applets to be signed, but this does carry some hazards. The security was put in place to protect you. It is best to complain to the website that they need to update their applet (especially banks, and other financial transactions).
Here is where you can get older Java for your Mac: http://www.oracle.com/technetwork/java/javase/downloads/java-archive-downloads-j avase7-521261.html#jdk-7u45-oth-JPR
You will need to accept the license agreement and create an oracle user's account to get these older downloads.
For some applications, such as those built into webcams, or other "internet of things" devices, you may have to check for firmware updates from the manufacturer, or there may be no other recourse but to use the older java in order to keep using those devices. There is, however, no easy way to "switch" javas back and forth using the older one when needed, and the newest one to be safest.
HTH.
