503 Errors randomly come up.

I am still getting 503 errors randomly on my website.
http://stellarealtygroup.com/

It seems more common when uploading or updating a page in the admin area but sometimes it happens when viewing the website as well.

We have deleted all unnecessary plugins. I have ran the plugin P3 (Plugin Performance Profiler)
These were the results.
WordPress Plugin Profile Report
===========================================
Report date: January 16, 2017
Theme name: Lava
Pages browsed: 11
Avg. load time: 0.5107 sec
Number of plugins: 12
Plugin impact: 22.42% of load time
Avg. plugin time: 0.1145 sec
Avg. core time: 0.3082 sec
Avg. theme time: 0.0866 sec
Avg. mem usage: 26.48 MB
Avg. ticks: 1,174
Avg. db queries : 88.64
Margin of error : 0.0013 sec

Plugin list:
===========================================
P3 (Plugin Performance Profiler) - 0.0529 sec - 46.22%
IMPress for IDX Broker - 0.0071 sec - 6.22%
Widgetkit - 0.0241 sec - 21.08%
Wp Rokcommon - 0.0030 sec - 2.61%
Contact Form 7 - 0.0013 sec - 1.14%
Embed Code - 0.0066 sec - 5.77%
Redirection - 0.0027 sec - 2.39%
Wp Smush Pro - 0.0021 sec - 1.79%
SmartCrawl - 0.0080 sec - 6.96%
Easy FancyBox - 0.0013 sec - 1.10%
Wp Roksprocket - 0.0054 sec - 4.71%
Cms Tree Page View - 0.0000 sec - 0.00%

Which doesn't seem out of the ordinary to me.

I contacted the hosting company with 0 luck. They said to run that plugin and delete whatever plugin caused the issue....

I have given support access.
I have done all I can to troubleshoot the issue with no luck.

Please help, I am willing to pay. At this point I just need this fixed.

Thank you,
Matt